Question

\(\left(x^2-4\right)^2+x=4\)

Answer 1

Đặt \(x^2-4=a\Rightarrow4=x^2-a\) ta được:

\(a^2+x=x^2-a\)

\(\Leftrightarrow a^2-x^2+x+a=0\)

\(\Leftrightarrow\left(a-x\right)\left(a+x\right)+x+a=0\)

\(\Leftrightarrow\left(a+x\right)\left(a-x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a+x=0\\a-x+1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2+x-4=0\\x^2-x-3=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\frac{-1\pm\sqrt{17}}{2}\\x=\frac{1\pm\sqrt{13}}{2}\end{matrix}\right.\)