Question

Solve the following quadratic equations by factorisation:

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

Answer 1

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