Giải pt:$13[(x^2-3x+6)^2+(x^2-2x+7)^2]=(5x^2-12x+33)^2$.
a/d bđt.... –  Hà Hoa 02-06-16 08:01 AM
pt $\Leftrightarrow (4+9)((x^{2}-3x+6)^{2} +(x^{2}-2x+7)^{2})=(2(x^{2}-3x+6)+3(x^{2}-2x+7))^{2}$
  AD BĐT BUNHIACOP.....
VT$\geq (2(x^{2}-3x+6)+3(x^{2}-2x+7))^{2}=VP$ (1)
pt $\Leftrightarrow$ (1) xảy ra dấu "=" 
$\Leftrightarrow 3(x^{2}-3x+6)=2(x^{2}-2x+7)$
 $\Leftrightarrow x=1 or x=4$

có. lag v lun –  Nguyễn Nhung 04-06-16 09:47 PM
sao lag thế >.>, chỗ bà có lag vậy ko? –  Confusion 04-06-16 09:43 PM
$\Leftrightarrow 13[(x^4-6x^3+21x^2-36x+36)+(x^4-4x^3+18x^2-28x+49)]=25x^4-120x^3+474x^2-792x+1089$
$\Leftrightarrow 13(2x^4-10x^3+39x^2-64x+85)=25x^4-....+1089$
$\Leftrightarrow 26x^4-130x^3+507x^2-832x+1105=25x^4-...+1089$
$\Leftrightarrow x^4-10x^3+33x^2-40+16=0$
$\Leftrightarrow (x-4)^2(x-1)^2=0$
xong

ế 2 chú = tủi nhỉ :D –  Confusion 02-06-16 09:21 AM
bó tay :)) –  tran85295 02-06-16 09:04 AM
Phương trình cần giải tương đương với $13[(x^2-3x+6)^2+(x^2-2x+7)^2]=[2(x^2-3x+6)+3(x^2-2x+7)]^2$,
hay $[3(x^2-3x+6)-2(x^2-2x+7)]^2=0$,
hay $3(x^2-3x+6)-2(x^2-2x+7)=0$,
hay $x^2-5x+4=0$,
hay $x=1\vee x=4$.
Vậy phương trình đã cho có hai nghiệm phân biệt, đó là $x=1$ hoặc $x=4$.

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