Solve each of the following quadratic equations:

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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