Question

Solve the following quadratic equations by factorisation:
$x^2-\left(\sqrt{3}+1\right)x+\sqrt{3}=0$

Answer 1

Consider the equation $x^2-\left(\sqrt{3}+1\right)x+\sqrt{3}=0$
$$\begin{gathered} \Rightarrow x^2-(\sqrt{3}+1)x+\sqrt{3}=0 \\ \Rightarrow x^2-\sqrt{3}x-x+\sqrt{3}=0 \\ \Rightarrow x\left(x-\sqrt{3}\right)-1\left(x-\sqrt{3}\right)=0 \\ \Rightarrow \left(x-\sqrt{3}\right)\left(x-1\right)=0 \\ \Rightarrow \left(x-\sqrt{3}\right)=0\mathrm{or}\left(x-1\right)=0 \\ \Rightarrow x=\sqrt{3}\mathrm{or}x=1 \end{gathered}$$