Question

rút gọn

a)\(\sqrt{x-1-2\sqrt{x-2}}+\sqrt{x-1+2\sqrt{x-2}}\)

b)\(\sqrt{x^2-4x+4}+\frac{x-2}{\sqrt{x^2-4x+4}}\)

Answer 1

ĐKXĐ: bạn tự tìm

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

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

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

\(=\left[{}\begin{matrix}2\sqrt{x-2}\left(x\ge3\right)\\2\left(2\le x< 3\right)\end{matrix}\right.\)

\(B=\sqrt{\left(x-2\right)^2}+\frac{x-2}{\sqrt{\left(x-2\right)^2}}=\left|x-2\right|+\frac{x-2}{\left|x-2\right|}\)

\(=\left[{}\begin{matrix}x-1\left(x>2\right)\\1-x\left(x< 2\right)\end{matrix}\right.\)