Đáp án:
\(\left[ \begin{array}{l}x=2\\x=\frac{5}{2}\end{array} \right.\)
Giải thích các bước giải:
`x^2-4x+4=8(x-2)^5`
`<=> (x-2)^2=8(x-2)^5`
`<=> 8(x-2)^5-(x-2)^2=0`
`<=> (x-2)^2[8(x-2)^3-1]=0`
`<=> (x-2)^2[8(x^3-6x^2+12x-8)-1]=0`
`<=> (x-2)^2(8x^3-48x^2+96x-64-1]=0`
`<=> (x-2)^2(8x^3-48x^2+96x-65)=0`
`<=> (x-2)^2(8x^3-20x^2-28x^2+70x+26x-65)=0`
`<=> (x-2)^2[4x^2(2x-5)-14x(2x-5)+26(2x-5)]=0`
`<=> (x-2)^2(2x-5)(4x^2-14x+26)=0`
do `4x^2-14x+26=(2x)^2-2.2x. 7/2+49/4+55/4=(2x-7/2)^2+55/4>=55/4>0`
`=>`\(\left[ \begin{array}{l}x-2=0\\2x-5=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=2\\x=\frac{5}{2}\end{array} \right.\)
