Question:
Solve each of the following quadratic equations:
$x^{2}-(1+\sqrt{2}) x+\sqrt{2}=0$
Solution:
$x^{2}-(1+\sqrt{2}) x+\sqrt{2}=0$
$x^{2}-x-\sqrt{2} x+\sqrt{2}=0$
$x(x-1)-\sqrt{2}(x-1)=0$
$(x-\sqrt{2})(x-1)=0$
$\Rightarrow x-\sqrt{2}=0$ and $x-1=0$
$\Rightarrow x=\sqrt{2}$ and $x=1$
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