Đáp án:

Giải thích các bước giải:

 `x^4-4x^2(2x-1)-12(2x-1)^2=0`

`<=>36(2x-1)^2+12x^2(2x-1)-3x^4=0`

`<=>[36(2x-1)^2+12x^2(2x-1)+x^4]-4x^4=0`

`<=>(x^2+12x-6)^2-(2x^2)^2=0`

`<=>(x^2-12x+6)(x^2+4x-2)=0`

`=>`$\left[\begin{matrix}x^2-12x+6=0\\x^2+4x-2=0\end{matrix}\right.$

`=>`$\left[\begin{matrix}(x-6)^2=30\\(x+2)^2=6\end{matrix}\right.$

*Nếu `(x-6)^2=30`

`=>`$\left[\begin{matrix}x-6=\sqrt{30}\\x-6=-\sqrt{30}\end{matrix}\right.$

`=>`$\left[\begin{matrix}x=6+\sqrt{30}\\x=6-\sqrt{30}\end{matrix}\right.$

*Nếu `(x+2)^2=6`

`=>`$\left[\begin{matrix}x+2=\sqrt{6}\\x+2=-\sqrt{6}\end{matrix}\right.$

`=>`$\left[\begin{matrix}x=-2+\sqrt{6}\\x=-2-\sqrt{6}\end{matrix}\right.$