Question

giải phương trình: \(x^2+\frac{x^2}{\left(x+1\right)^2}=3\)

Answer 1

\(x\ne-1\)

\(x^2-2x.\frac{x}{x+1}+\left(\frac{x}{x+1}\right)^2+2x.\frac{x}{x+1}-3=0\)

\(\Leftrightarrow\left(x-\frac{x}{x+1}\right)^2+2\frac{x^2}{x+1}-3=0\)

\(\Leftrightarrow\left(\frac{x^2}{x+1}\right)^2+2\frac{x^2}{x+1}-3=0\)

\(\Rightarrow\left[{}\begin{matrix}\frac{x^2}{x+1}=1\\\frac{x^2}{x+1}=-3\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-x-1=0\\x^2+3x+3=0\left(vn\right)\end{matrix}\right.\) \(\Rightarrow x=\frac{1\pm\sqrt{5}}{2}\)