Question

Giải phương trình: \(\left(X^2-2X\right)^2+3X^2-6X=-2\)

Giúp mk vs nha

Answer 1

Đặt \(x^2-2x=a\)

\(\Rightarrow a^2+3a=-2\Leftrightarrow a^2+3a+2=0\)

\(\Rightarrow\left[{}\begin{matrix}a=-1\\a=-2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x^2-2x=-1\\x^2-2x=-2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x^2-2x+1=0\\x^2-2x+2=0\left(vn\right)\end{matrix}\right.\)

\(\Rightarrow x=1\)

Answer 2

Đặt $x^2-2x=a$

$\Rightarrow a^2+3a=-2\iff a^2+3a+2=0$

$\Rightarrow [\begin{array}{c}a=-1\\ a=-2\end{array}$ $\Rightarrow [\begin{array}{c}{x}^2-2x=-1\\ x^2-2x=-2\end{array}$ $\Rightarrow [\begin{array}{c}{x}^2-2x+1=0\\ x^2-2x+2=0(\mathrm{vô\; nghiệm)}\end{array}$

$\Rightarrow x=1$