Question

Solve for $x:x^2-\left(\sqrt{3}+1\right)x+\sqrt{3}=0.$

Answer 1

$x^2-(\sqrt{3}+1)x+\sqrt{3}=0$

$\Rightarrow x^2-x-\sqrt{3}x+\sqrt{3}=0$

$\Rightarrow x(x-1)-\sqrt{3}(x-1)=0$

$\Rightarrow (x-1)(x-\sqrt{3})=0$

$x=1$ or $x=\sqrt{3}$