Question

GIẢI PHƯƠNG TRÌNH 

\(\sqrt{x^2-4x+4}\) +2=x

Answer 1

\(\sqrt{x^2-4x+4}+2=x\\ \Leftrightarrow\sqrt{\left(x-2\right)^2}+2=x\\ \Leftrightarrow x-2+2=x\\ \Leftrightarrow x-2=x-2\left(đúng\right)\)

Answer 2

\(\sqrt{x^2-4x+4}+2=x\\ \Leftrightarrow\sqrt{\left(x-2\right)^2}=x-2\\ \Leftrightarrow\left|x-2\right|=x-2\\ TH_1:x>2\\ x-2=x-2\left(LD\forall x\right)\\ TH_2:x\le2\\ -x+2=x-2\Leftrightarrow-2x=-4\Leftrightarrow x=2\left(tm\right)\)

Vậy \(S=\left\{2\right\}\)