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Square of (√5+√3/√5-√3)+square of(√5-√3/√5+√3)

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Step by STEP Explanation:-

( \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } ) {}^{2} + ( \frac{ \sqrt{5 } - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } ) {}^{2} \\ = \frac{(\sqrt{5} + \sqrt{3}) {}^{2} }{(\sqrt{5} - \sqrt{3}) {}^{2} } + \frac{(\sqrt{5} - \sqrt{3}) {}^{2} }{(\sqrt{5} + \sqrt{3}) {}^{2} } \\ = \frac{5 + 2 \sqrt{15} + 3 }{5 - 2 \sqrt{15} + 3 } + \frac{5 - 2 \sqrt{15} + 3 }{5 + 2 \sqrt{15} + 3 } \\ = \frac{8 + 2 \sqrt{15} }{8 - 2 \sqrt{15} } + \frac{8 - 2 \sqrt{15} }{8 + 2 \sqrt{15} } \\ = \frac{(8 + 2 \sqrt{15} ) {}^{2} + (8 - 2 \sqrt{15} ) {}^{2} }{(8 - 2 \sqrt{15} )(8 + 2 \sqrt{15} )} \\ = \frac{(64 + 32 \sqrt{15} + 60) + 64 - 32 \sqrt{15} + 60}{64 - 60} \\ = \frac{124 + 32 \sqrt{15} + 124 - 32 \sqrt{15} }{4} \\ = \frac{248}{4} \\ = 62

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