Question

Solve; $x(x-1)=1$

Answer 1

$x(x-1)-1=0$

$\Rightarrow x^2-x-1=0$

$x=\frac{1\begin{array}{c}+\\ -\end{array}\sqrt{1-(4\times 1\times -1)}}{2\times 1}=\frac{1\begin{array}{c}+\\ -\end{array}\sqrt{1+4}}{2}$

$x_1=\frac{1+\sqrt{5}}{2}{x}_2=\frac{1-\sqrt{5}}{2}$