Question

giải các phương  trình

\(\sqrt{x^2-2x+1}-7=0\)

 

Answer 1

\(\sqrt{x^2-2x+1}-7=0\left(1\right)\)

\(\Leftrightarrow\sqrt{\left(x-1\right)^2}=7\Leftrightarrow\left|x-1\right|=7\)

TH1: \(x\ge1\)

\(\left(1\right)\Leftrightarrow x-1=7\Leftrightarrow x=8\)

TH2: \(x< 1\)

\(\left(1\right)\Leftrightarrow1-x=7\Leftrightarrow x=-6\)

Answer 2

Ta có: \(\sqrt{x^2-2x+1}-7=0\)

\(\Leftrightarrow\left|x-1\right|=7\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=7\\x-1=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-6\end{matrix}\right.\)