Question

Giải pt:

\(x-\sqrt{x^4-2x^2+1}=1\)

Answer 1

\(\Leftrightarrow\) x - \(\sqrt{\left(x^2-1\right)^2}\) = 1 ( ĐKXĐ : \(\left(x^2-1\right)^2\) \(\ge0\) luôn đúng \(\forall x\) )

\(\Leftrightarrow\) x - \(x^2\) + 1 = 1

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

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

\(\Leftrightarrow\) \(\left[{}\begin{matrix}x=0\\1-x=0\end{matrix}\right.\) \(\Leftrightarrow\) \(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

Vậy x = {0;1}