Question

giải phương trình

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

Answer 1

ĐKXĐ: \(x\ge\dfrac{2}{3}\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\\dfrac{1}{\sqrt{3x-2}+\sqrt{x+1}}=x+1\left(1\right)\end{matrix}\right.\)

Do \(x\ge\dfrac{2}{3}\Rightarrow\left\{{}\begin{matrix}VT< 1\\VP>1\end{matrix}\right.\) \(\Rightarrow\left(1\right)\) vô nghiệm

Vậy pt có nghiệm duy nhất \(x=\dfrac{3}{2}\)