Given $a = 3 + 2 \sqrt{2}$ , find the value of $(\sqrt{a} - \frac{1}{\sqrt{a}})$ .

Created: 2 months ago | Updated: 2 months ago

Job Solution Janata Bank Ltd Janata Bank Ltd. Recruitment Test AEO ( RC) Written Examination Held On : 22.09.2017 || 2017 গণিত

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

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