Question

\(\sqrt{x^2-x-6}=\sqrt{x-3}\)

Answer 1

ĐKXĐ: x>=3

PT =>x^2-x-6=x-3

=>x^2-2x-3=0

=>(x-3)(x+1)=0

=>x=-1(loại) hoặc x=3(nhận)

Answer 2

\(\sqrt{x^2-x-6}=\sqrt{x-3}\) ĐK: \(x\ge3\)

\(\Leftrightarrow\sqrt{\left(x^2-x-6\right)^2}=\sqrt{\left(x-3\right)^2}\)

\(\Leftrightarrow x^2-x-6=x-3\) 

\(\Leftrightarrow x^2-x-x-6+3=0\)

\(\Leftrightarrow x^2-2x-3=0\)

\(\Leftrightarrow\left(x+1\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\left(\text{loại}\right)\\x=3\left(\text{TM}\right)\end{matrix}\right.\)

Vậy \(S=\left\{3\right\}\).