Question

giải phương trình sau :

\(3x^2+x+\frac{3}{x^2}+\frac{1}{x}-8=0\)

Answer 1

ĐKXĐ: \(x\ne0\)

\(\Leftrightarrow3\left(x^2+\frac{1}{x^2}\right)+x+\frac{1}{x}-8=0\)

Đặt \(x+\frac{1}{x}=t\Rightarrow x^2+\frac{1}{x^2}=t^2-2\)

\(\Leftrightarrow3\left(t^2-2\right)+t-8=0\)

\(\Leftrightarrow3t^2+t-14=0\Rightarrow\left[{}\begin{matrix}t=2\\t=-\frac{7}{3}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\frac{1}{x}=2\\x+\frac{1}{x}=-\frac{7}{3}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-2x+1=0\\3x^2+7x+3=0\end{matrix}\right.\) (casio)