Question

Answer It This Math problem ​

Answer 1

Answer:

hope it helps you ⬆️

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Answer 2

Answer:

2

Check these calculation

$x \\ = 3 + 2 \sqrt{2} \\ = 1 + 2 + 2 \sqrt{2} \\ = {1}^{2} + (\sqrt{2} ) {}^{2} + 2(1) \sqrt{2} \\ if \: \: u \: \: know \: \: \\ {a}^{2} + {b}^{2} + 2ab = (a + b) {}^{2} \\ so \\ x = ( \sqrt{2} + 1) {}^{2} \\ and \\ \sqrt{x} = \sqrt{2} + 1 \\ now\\ \frac{1}{ \sqrt{x} } = \frac{1}{ \sqrt{2} + 1 } \times \frac{ \sqrt{2} - 1 }{ \sqrt{2} - 1 } \\ \{rationaliation \\ \frac{1}{ \sqrt{x} } = \frac{ \sqrt{2} - 1}{ { \sqrt{2} }^{2} - {1}^{2} } \\ since \: \: (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ \frac{1}{ \sqrt{x} } = \frac{ \sqrt{2} - 1 }{2 - 1} = \sqrt{2} - 1 \\ \\ so \\ \\ \sqrt{x} - \frac{1}{ \sqrt{x} } \\ \\ = \sqrt{2} + 1 - ( \sqrt{2} - 1) \\ = \sqrt{2} + 1 - \sqrt{2} + 1 \\ = 2$