\(x^2-x-1=x^2-2.\frac{1}{2}x+\frac{1}{4}-\frac{5}{4}\)
\(\Leftrightarrow\left(x-\frac{1}{2}\right)^2-\frac{5}{4}=0\)
\(\Leftrightarrow\left(x-\frac{1}{2}\right)^2=\frac{5}{4}\)
Khai căn hai vế ra ta được
\(x-\frac{1}{2}=\frac{\sqrt{5}}{2}\)
\(\Leftrightarrow x=\frac{\sqrt{5}}{2}+\frac{1}{2}\)
\(\Leftrightarrow x=1,618033989\)