x ^ 2 ( √( 2 ) +1 ) x+√( 2 ) =0 ⇒ x ^ 2 √( 2 ) x x+√( 2 ) =0 ⇒ x( x √( 2 ) #160; ) 1( x √( 2 ) #160; ) =0 ⇒( x √( 2 ) #160; ) ( x 1 ...

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Solving a Quadratic Equation by Completion of Squares Method

Evaluate x2...

Question

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

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Solution

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

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