Question

Giải phương trình: \(x^2-12+\frac{36}{x^2}-4x+\frac{24}{x}=5\)

Answer 1

ĐKXĐ:...

\(x^2+\frac{36}{x^2}-4\left(x-\frac{6}{x}\right)-17=0\)

Đặt \(x-\frac{6}{x}=a\Rightarrow a^2=x^2+\frac{36}{x^2}-12\Rightarrow x^2+\frac{36}{x^2}=a^2+12\)

\(a^2+12-4a-17=0\)

\(\Leftrightarrow a^2-4a-5=0\Rightarrow\left[{}\begin{matrix}a=-1\\a=5\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x-\frac{6}{x}=-1\\x-\frac{6}{x}=5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2+x-6=0\\x^2-5x-6=0\end{matrix}\right.\)