Question

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

Answer 1

ĐKXĐ: ...

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

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

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

Đặt \(\frac{x^2}{x+1}=a\Rightarrow a^2+2a-3=0\Rightarrow\left[{}\begin{matrix}a=1\\a=-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\frac{x^2}{x+1}=1\\\frac{x^2}{x+1}=-3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x^2-x-1=0\\x^2+3x+3=0\end{matrix}\right.\)(casio)