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giải đáp
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BDT 2
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Lời giải này có yêu cầu trả vỏ sò để xem. Bạn hãy link trên để vào xem chi tiết
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giải đáp
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BDT 1
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b/ Ta có: $TH1: 1-2x<0\Leftrightarrow x>\frac{1}{2}\Rightarrow bpt$ luôn đúng (Vì $\sqrt{4x^2-4x+3}>0\forall x; 1-2x<0)$ $TH2: 1-2x\geq 0\Leftrightarrow x\leq\frac{1}{2}\Rightarrow bpt\Leftrightarrow 4x^2-4x+3>4x^2-4x+1\Leftrightarrow 2>0 (luôn đúng)\Rightarrow đpcm$ |
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giải đáp
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BDT 1
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a/ $TH1: x<0\Rightarrow x+|x|=x-x=0\geq0$ $TH2: x\geq 0\Rightarrow x+|x|=x+x=2x\geq0\Rightarrow đpcm$
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được thưởng
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Đăng nhập hàng ngày 14/02/2017
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được thưởng
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Đăng nhập hàng ngày 12/02/2017
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được thưởng
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Đăng nhập hàng ngày 09/02/2017
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sửa đổi
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phương trình vô tỉ
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phương trình vô tỉ 4x^{3}= căn của 1-x^2
phương trình vô tỉ $4x^{3}= \sqrt{1-x^2 }$
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sửa đổi
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cần gấp
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S2−8S+4m−3=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; color: rgb(40, 40, 40); font-family: helvetica, arial, sans-serif; position: relative; background-color: rgb(247, 247, 247);">DK: x∈[−12,12],m≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x∈[−12,12],m≥0x∈[−12,12],m≥0Đặt a=1−2x,b=1+2x=>x2=1−ab4" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">a=√1−2x,b=√1+2x=>x2=1−ab4a=1−2x,b=1+2x=>x2=1−ab4Ta có hệ: {a2+b2=2a+b+1−ab4=m" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">{a2+b2=2a+b+1−ab4=m{a2+b2=2a+b+1−ab4=mTiếp tục đặt S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)Nhân (2) với 2 rồi trừ (1) ta có ptr S2−8S+4m−3=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">S2−8S+4m−3=0S2−8S+4m−3=0Xét hàm số f(x)=x2+1−2x+1+2x" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f(x)=x2+√1−2x+√1+2xf(x)=x2+1−2x+1+2xf′(x)=2x−11−2x+11+2x" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)=2x−1√1−2x+1√1+2xf′(x)=2x−11−2x+11+2x=x(2+41−2x1+2x(1+2x+1−2x))" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">=x(2+4√1−2x√1+2x(√1+2x+√1−2x))=x(2+41−2x1+2x(1+2x+1−2x))f′(x)=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)=0f′(x)=0 khi và chỉ khi x=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x=0x=0Do đó ta có Bảng biến thiên (tự vẽ)+Nếu x≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x≥0x≥0 thì f′(x)≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)≥0f′(x)≥0 suy ra ....+Nếu x≤0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x≤0x≤0 thì f′(x)≤0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)≤0f′(x)≤0 suy ra ....Tóm lại là, từ bảng biến thiên ta được:m≤f(0)=2" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">m≤f(0)=2m≤f(0)=2
S2−8S+4m−3=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; color: rgb(40, 40, 40); font-family: helvetica, arial, sans-serif; position: relative; background-color: rgb(247, 247, 247);">DK: x∈[−12,12],m≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x∈[−12,12],m≥0x∈[−12,12],m≥0Đặt a=1−2x,b=1+2x=>x2=1−ab4" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">a=√1−2x,b=√1+2x=>x2=1−ab4a=1−2x,b=1+2x=>x2=1−ab4Ta có hệ: {a2+b2=2a+b+1−ab4=m" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">{a2+b2=2a+b+1−ab4=m{a2+b2=2a+b+1−ab4=mTiếp tục đặt S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)Nhân (2) với 2 rồi trừ (1) ta có ptr S2−8S+4m−3=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">S2−8S+4m−3=0S2−8S+4m−3=0Xét hàm số f(x)=x2+1−2x+1+2x" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f(x)=x2+√1−2x+√1+2xf(x)=x2+1−2x+1+2xf′(x)=2x−11−2x+11+2x" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)=2x−1√1−2x+1√1+2xf′(x)=2x−11−2x+11+2x=x(2+41−2x1+2x(1+2x+1−2x))" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">=x(2+4√1−2x√1+2x(√1+2x+√1−2x))=x(2+41−2x1+2x(1+2x+1−2x))f′(x)=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)=0f′(x)=0 khi và chỉ khi x=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x=0x=0Do đó ta có Bảng biến thiên (tự vẽ)+Nếu x≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x≥0x≥0 thì f′(x)≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)≥0f′(x)≥0 suy ra ....+Nếu x≤0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x≤0x≤0 thì f′(x)≤0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)≤0f′(x)≤0 suy ra ....Tóm lại là, từ bảng biến thiên ta được:m≤f(0)=2" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">m≤f(0)=2m≤f(0)=2
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sửa đổi
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cần gấp
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S2−8S+4m−3=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; color: rgb(40, 40, 40); font-family: helvetica, arial, sans-serif; position: relative; background-color: rgb(247, 247, 247);">DK: x∈[−12,12],m≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x∈[−12,12],m≥0x∈[−12,12],m≥0Đặt a=1−2x,b=1+2x=&gt;x2=1−ab4" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">a=√1−2x,b=√1+2x=>x2=1−ab4a=1−2x,b=1+2x=>x2=1−ab4Ta có hệ: {a2+b2=2a+b+1−ab4=m" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">{a2+b2=2a+b+1−ab4=m{a2+b2=2a+b+1−ab4=mTiếp tục đặt S=a+b,P=ab=&gt;{S2−2P=2(1)4S−P=4m−1(2)" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)Nhân (2) với 2 rồi trừ (1) ta có ptr S2−8S+4m−3=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">S2−8S+4m−3=0S2−8S+4m−3=0Xét hàm số f(x)=x2+1−2x+1+2x" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f(x)=x2+√1−2x+√1+2xf(x)=x2+1−2x+1+2xf′(x)=2x−11−2x+11+2x" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)=2x−1√1−2x+1√1+2xf′(x)=2x−11−2x+11+2x=x(2+41−2x1+2x(1+2x+1−2x))" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">=x(2+4√1−2x√1+2x(√1+2x+√1−2x))=x(2+41−2x1+2x(1+2x+1−2x))f′(x)=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)=0f′(x)=0 khi và chỉ khi x=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x=0x=0Do đó ta có Bảng biến thiên (tự vẽ)+Nếu x≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x≥0x≥0 thì f′(x)≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)≥0f′(x)≥0 suy ra ....+Nếu x≤0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x≤0x≤0 thì f′(x)≤0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)≤0f′(x)≤0 suy ra ....Tóm lại là, từ bảng biến thiên ta được:m≤f(0)=2" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">m≤f(0)=2m≤f(0)=2
S2−8S+4m−3=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; color: rgb(40, 40, 40); font-family: helvetica, arial, sans-serif; position: relative; background-color: rgb(247, 247, 247);">DK: x∈[−12,12],m≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x∈[−12,12],m≥0x∈[−12,12],m≥0Đặt a=1−2x,b=1+2x=>x2=1−ab4" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">a=√1−2x,b=√1+2x=>x2=1−ab4a=1−2x,b=1+2x=>x2=1−ab4Ta có hệ: {a2+b2=2a+b+1−ab4=m" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">{a2+b2=2a+b+1−ab4=m{a2+b2=2a+b+1−ab4=mTiếp tục đặt S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)S=a+b,P=ab=>{S2−2P=2(1)4S−P=4m−1(2)Nhân (2) với 2 rồi trừ (1) ta có ptr S2−8S+4m−3=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">S2−8S+4m−3=0S2−8S+4m−3=0Xét hàm số f(x)=x2+1−2x+1+2x" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f(x)=x2+√1−2x+√1+2xf(x)=x2+1−2x+1+2xf′(x)=2x−11−2x+11+2x" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)=2x−1√1−2x+1√1+2xf′(x)=2x−11−2x+11+2x=x(2+41−2x1+2x(1+2x+1−2x))" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">=x(2+4√1−2x√1+2x(√1+2x+√1−2x))=x(2+41−2x1+2x(1+2x+1−2x))f′(x)=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)=0f′(x)=0 khi và chỉ khi x=0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x=0x=0Do đó ta có Bảng biến thiên (tự vẽ)+Nếu x≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x≥0x≥0 thì f′(x)≥0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)≥0f′(x)≥0 suy ra ....+Nếu x≤0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">x≤0x≤0 thì f′(x)≤0" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">f′(x)≤0f′(x)≤0 suy ra ....Tóm lại là, từ bảng biến thiên ta được:m≤f(0)=2" role="presentation" style="display: inline-block; line-height: 0; font-size: 14.04px; word-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px; position: relative; background-color: rgb(247, 247, 247);">m≤f(0)=2m≤f(0)=2
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sửa đổi
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$\color{red}{Happy}$ $\color{red}{ New}$ $\color{red}{ Year} $ $\color{red}{2017 ! }$
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|ab|$\times$|ab|=|cab| $\Rightarrow |ab|^{2}=|cab|$ vì |cab| là số có ba chữ số $\Rightarrow 100\leq |cab|\leq 999\Rightarrow 100\leq |ab|^{2}\leq 999\Rightarrow 10\leq |ab|\leq 31\Rightarrow a=1;2;3$mà $|ab|^{2}=|cab|\Rightarrow b=0;1;5;6$$\Rightarrow |ab|=10;11;15;16;20;21;25;26;30;31$Thử lần lượt ta có :a=2;b=5;c=6
$\overline{ab}.\overline{ab}=\overline{cab} \Rightarrow \overline {ab}^{2}=\overline{cab}$ Vì $\overline{cab}$ là số có ba chữ số $\Rightarrow 100\leq \overline{cab}\leq 999\Rightarrow 100\leq \overline{ab}^{2}\leq 999\Rightarrow 10\leq \overline{ab}\leq 31\Rightarrow a=1;2;3$mà $\overline{ab}^{2}=\overline{cab}\Rightarrow b=0;1;5;6$$\Rightarrow \overline{ab}=10;11;15;16;20;21;25;26;30;31$Thử lần lượt ta có :$a=2;b=5;c=6$
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sửa đổi
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Happy new year
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f(x=$x^2$ +$\frac{1}{x}$+$\frac{1}{x}$rồi áp dụng AM-GM là ra
$f(x)=x^2 +\frac{1}{x}+\frac{1}{x}$rồi áp dụng AM-GM là ra
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sửa đổi
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Dai so 7
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Dai so 7 CMRA=220^11969+119^69220+69^220119 chia hết cho 102
Dai so 7 CMR $A=220^ {11969 }+119^ {69220 }+69^ {220119 }$ chia hết cho $102 $
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