Question

\(\sqrt{x-1}\) = \(\sqrt{5x-1}\) - \(\sqrt{3x-2}\)

Answer 1

\(\sqrt{x-1}=\sqrt{5x-1}-\sqrt{3x-2}\)(1)

ĐKXĐ:\(x\ge1\)

(1)\(\Leftrightarrow\sqrt{x-1}+\sqrt{3x-2}=\sqrt{5x-1}\)\(\Leftrightarrow x-1+3x-2+2\sqrt{\left(x-1\right)\left(3x-2\right)}=5x-1\)

\(\Leftrightarrow2\sqrt{\left(x-1\right)\left(3x-2\right)}=x+2\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-2\\4\left(x-1\right)\left(3x-2\right)=x^2+4x+4\end{matrix}\right.\)

+) \(4\left(x-1\right)\left(3x-2\right)=x^2+4x+4\Leftrightarrow11x^2-24x+4=0\)\(\Leftrightarrow\left\{{}\begin{matrix}x=2\left(tm\right)\\x=\frac{2}{11}\left(l\right)\end{matrix}\right.\)

Vậy phương trình có nghiệm x = 2