Question

Solve each of the following equation by using the method of completing the square:
$x^2-(\sqrt{2}+1)x+\sqrt{2}=0$

Answer 1

Given,

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

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

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

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

$\therefore x=1,\sqrt{2}$