Question

If x=3+ 2 under root 2 then find the value of root x minus one upon root x

Answer 1

$\textbf{Answer :}$

$Now, \\ \\ x = 3 + 2 \sqrt{2} \\ \\ = 1 + 2 \sqrt{2} + 2 \\ \\ = {1}^{2} + (2 \times 1 \times \sqrt{2} ) + {( \sqrt{2} )}^{2} \\ \\ = {(1 + \sqrt{2} )}^{2} \\ \\ = {( \sqrt{2} + 1)}^{2} \\ \\ So, \: \: \sqrt{x} = \sqrt{2} + 1 \\ \\ Then, \: \: \frac{1}{ \sqrt{x} } \\ \\ = \frac{1}{ \sqrt{2} + 1} \\ \\ = \frac{( \sqrt{2} - 1) }{( \sqrt{2} + 1)( \sqrt{2} - 1)} \\ \\ = \frac{ \sqrt{2} - 1 }{2 - 1} \\ \\ = \frac{ \sqrt{2} - 1 }{1} \\ \\ = \sqrt{2} - 1 \\ \\ Therefore, \\ \\ \sqrt{x} - \frac{1}{ \sqrt{x} } \\ \\ = ( \sqrt{2} + 1) - ( \sqrt{2} - 1) \\ \\ = \sqrt{2} + 1 - \sqrt{2} + 1 \\ \\ = 2$

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Answer 2

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