Given a=3+22, find the value of a-1a.

Shohan

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2025-01-04 04:42

1 Answers

Shohan

$G i v e n, a = 3 + 2 \sqrt{2} \Rightarrow a = 2 + 1 + 2 \sqrt{2} \Rightarrow a = {\sqrt{(2)}}^{2} + 2 \times \sqrt{2} \times 1 + 1^{2} \Rightarrow a = {(\sqrt{2} + 1)}^{2} \Rightarrow \sqrt{a} = \sqrt{2} + 1 a n d, \frac{1}{\sqrt{a}} = \frac{1}{\sqrt{2} + 1} = \frac{\sqrt{2} - 1}{(\sqrt{2} + 1) (\sqrt{2} - 1)} = \frac{\sqrt{2} - 1}{{(\sqrt{2})}^{2} - {(1)}^{2}} = \frac{\sqrt{2} - 1}{2 - 1} = \sqrt{2} - 1 N o w, (\sqrt{a} - \frac{1}{\sqrt{a}}) = \sqrt{2} + 1 - \sqrt{2} + 1 = 2 [[P u t t i n g t h e v a l u e o f \sqrt{a} a n d \frac{1}{\sqrt{a}}]$

Answer: 2

4 views Answered 2024-12-14 13:31

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