Question:
Solve the following quadratic equations by factorization:
$x^{2}-(\sqrt{2}+1) x+\sqrt{2}=0$
Solution:
We have been given
$x^{2}-(\sqrt{2}+1) x+\sqrt{2}=0$
$x^{2}-\sqrt{2} x-x+\sqrt{2}=0$
$x(x-\sqrt{2})-1(x-\sqrt{2})=0$
$(x-1)(x-\sqrt{2})=0$
Therefore,
$x-1=0$
$x=1$
or,
$x-\sqrt{2}=0$
$x=\sqrt{2}$
Hence, $x=1$ or $x=\sqrt{2}$.
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