Question

Tìm x giúp mik ạ

Answer 1

\(\sqrt{x^2-2x+1}=\sqrt{3+2\sqrt{2}}\)

\(\Leftrightarrow\sqrt{\left(x-1\right)^2}=\sqrt{\left(\sqrt{2}+1\right)^2}\)

\(\Leftrightarrow\left|x-1\right|=\sqrt{2}+1\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=\sqrt{2}+1\\x-1=-\sqrt{2}-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2+\sqrt{2}\\x=-\sqrt{2}\end{matrix}\right.\)

Answer 2

Lời giải:

PT $\Leftrightarrow \sqrt{(x-1)^2}=\sqrt{(\sqrt{2}+1)^2}$

$\Leftrightarrow |x-1|=|\sqrt{2}+1|=\sqrt{2}+1$

$\Leftrightarrow x-1=\pm (\sqrt{2}+1)$

$\Leftrightarrow x=2+\sqrt{2}$ hoặc $x=-\sqrt{2}$