Question

giải pt \(\frac{8}{5\left(x+2\right)}+\sqrt{\frac{5x+2}{x+2}}=\frac{11}{5}\)

Answer 1

ĐKXĐ: \(\left[{}\begin{matrix}x< -2\\x\ge-\frac{2}{5}\end{matrix}\right.\)

\(\Leftrightarrow\frac{8}{5\left(x+2\right)}-1+\sqrt{\frac{5x+2}{x+2}}-\frac{6}{5}=0\)

\(\Leftrightarrow\frac{-\left(5x+2\right)}{5\left(x+2\right)}+\sqrt{\frac{5x+2}{x+2}}-\frac{6}{5}=0\)

Đặt \(\sqrt{\frac{5x+2}{x+2}}=a\ge0\)

\(-\frac{1}{5}a^2+a-\frac{6}{5}=0\Leftrightarrow a^2-5a+6=0\)

\(\Rightarrow\left[{}\begin{matrix}a=2\\a=3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\frac{5x+2}{x+2}=4\\\frac{5x+2}{x+2}=9\end{matrix}\right.\) \(\Rightarrow...\)