Question

Giải phương trình:

(x² - 2x)² + (x - 1)² - 13 = 0

Answer 1

\(\Leftrightarrow\left(x^2-2x\right)^2+x^2-2x+1-13=0\)

\(\Leftrightarrow\left(x^2-2x\right)^2+x^2-2x-12=0\)

Đặt \(x^2-2x=t\Rightarrow t^2+t-12=0\Rightarrow\left[{}\begin{matrix}t=3\\t=-4\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x^2-2x=3\\x^2-2x=-4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-2x-3=0\\x^2-2x+4=0\left(vô-nghiệm\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=3\end{matrix}\right.\)