Question

x=3+2✓2 find ✓×+1 /✓×

Answer 1

Ans.

$x = 3 + 2 \sqrt{2} \\ = 1 + 2 \sqrt{2} + 2\\ = {1}^{2} +(2 \times 1 \times \sqrt{2} ) + ( { \sqrt{2} })^{2} \\ =( {1 + \sqrt{2} })^{2} \\ \\ so \: \sqrt{x} = 1 + \sqrt{2} \\ and \: \frac{1}{ \sqrt{x} } = \frac{1}{1 + \sqrt{2} } \\ = \frac{1 - \sqrt{2} }{(1 + \sqrt{2})(1 - \sqrt{2} )} \\ = \frac{1 - \sqrt{2} }{1 - 2} \\ = \frac{1 - \sqrt{2} }{ - 1} \\ = \sqrt{2} - 1$

So,
$\sqrt{x} + \frac{1}{ \sqrt{x} } \\ = (1 + \sqrt{2} ) + ( \sqrt{2} - 1) \\ = 2 \sqrt{2}$

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