Question

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

Answer 1

ĐKXĐ: \(x\ge\dfrac{3}{2}\)

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

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

Xét (1):

Do \(x\ge\dfrac{3}{2}\Rightarrow\left\{{}\begin{matrix}\sqrt{2x-3}\ge0\\\sqrt{x}\ge\sqrt{\dfrac{3}{2}}>\dfrac{1}{2}\end{matrix}\right.\)

\(\Rightarrow\sqrt{2x-3}+\sqrt{x}>\dfrac{1}{2}\)

\(\Rightarrow\left(1\right)\) vô nghiệm

Vậy pt có nghiệm duy nhất \(x=3\)