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

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Solution

Given:

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

$x - 1 = 0 \Rightarrow x = 1$

Hence, the roots of the equation are √2 and 1

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