Question

if x =√7+√6÷√7−√6then find the value of (x+1/x)2

Answer 1

Hello Mate!

$x = \frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} - \sqrt{6} } \times \frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} + \sqrt{6} } \\ \frac{ {( \sqrt{7} + \sqrt{6} )}^{2} }{7 - 6} = 7 + 6 + 2 \sqrt{42} \\ = 13 + 2 \sqrt{42} \\ \frac{1}{x} = \frac{1}{13 + 2 \sqrt{42} } \times \frac{13 - 2 \sqrt{42} }{13 - 2 \sqrt{42} } \\ = \frac{13 - 2 \sqrt{42} }{169 - (4 \times 42)} \\ = 13 - 2 \sqrt{42} \\ x + \frac{1}{x} \\ 13 + 2 \sqrt{42} + 13 - 2 \sqrt{42} = 26 \\ {(x + \frac{1}{x} )}^{2} = {26}^{2} = 676$

Hope u got it dear

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