Question

giải phương trình \(x^2+\frac{81x^2}{\left(x+9\right)^2}=40\)

Answer 1

ĐKXĐ: \(x\ne-9\)

\(x^2-\frac{18x^2}{x+9}+\frac{\left(9x\right)^2}{\left(x+9\right)^2}+\frac{18x^2}{x+9}-40=0\)

\(\Leftrightarrow\left(x-\frac{9x}{x+9}\right)^2+\frac{18x^2}{x+9}-40=0\)

\(\Leftrightarrow\left(\frac{x^2}{x+9}\right)^2+\frac{18x^2}{x+9}-40=0\)

Đặt \(\frac{x^2}{x+9}=a\Rightarrow a^2+18a-40=0\Rightarrow\left[{}\begin{matrix}a=2\\a=-20\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\frac{x^2}{x+9}=2\\\frac{x^2}{x+9}=-20\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-2x-18=0\\x^2+20x+180=0\left(vn\right)\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1+\sqrt{19}\\x=1-\sqrt{19}\end{matrix}\right.\)