Question

Giải phương trình: 3x^2-x-1=0

Answer 1

\(3x^2-x-1=0\)

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

\(\Leftrightarrow x^2-2\cdot x\cdot\frac{1}{6}+\frac{1}{36}-\frac{13}{36}=0\)

\(\Leftrightarrow\left(x-\frac{1}{6}\right)^2=\frac{13}{36}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\frac{1}{6}=\frac{\sqrt{13}}{6}\\x-\frac{1}{6}=-\frac{\sqrt{13}}{6}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\frac{1+\sqrt{13}}{6}\\x=\frac{1-\sqrt{13}}{6}\end{matrix}\right.\)

Vậy phương trình có nghiệm \(x=\frac{1\pm\sqrt{13}}{6}\)