Question

Tìm x

a,\(\sqrt{\left(2x-1\right)^2}-x=3\)

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

Answer 1

a: \(\Leftrightarrow\left|2x-1\right|=x+3\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>=-3\\\left(2x-1-x-3\right)\left(2x-1+x+3\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>=-3\\\left(x-4\right)\left(3x+2\right)=0\end{matrix}\right.\Leftrightarrow x\in\left\{-\dfrac{2}{3};4\right\}\)

b: \(\Leftrightarrow\sqrt{3x-6}=x-2\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>=2\\3x-6=\left(x-2\right)^2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=2\\\left(x-2\right)\left(x-5\right)=0\end{matrix}\right.\Leftrightarrow x\in\left\{2;5\right\}\)