Solve each of the following quadratic equations:

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

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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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