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