Question

Giải phương trình

\(\sqrt{5x-1}-\sqrt{x+2}=\frac{4x-3}{5}\)

Answer 1

ĐK: \(x\ge\frac{1}{5}\)

PT\(\Leftrightarrow\frac{4x-3}{\sqrt{5x-1}+\sqrt{x+2}}-\frac{4x-3}{5}=0\)

\(\Leftrightarrow\left(4x-3\right).\left(\frac{1}{\sqrt{5x-1}+\sqrt{x+2}}-\frac{1}{5}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{4}{3}\left(tm\right)\\\frac{1}{\sqrt{5x-1}+\sqrt{x+2}}=\frac{1}{5}\left(1\right)\end{matrix}\right.\)

Giải (1) \(\Leftrightarrow\sqrt{5x-1}+\sqrt{x+2}=5\)

\(\Leftrightarrow6x+1+2\sqrt{5x^2+9x-2}=25\)

\(\Leftrightarrow\sqrt{5x^3+9x-2}=12-3x\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\le4\\4x^2-81x+146=0\end{matrix}\right.\) \(\Rightarrow x=2\)

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