Question

Please solve this..........

Answer 1

$x = \frac{3 + \sqrt{7} }{2} \\ {x}^{2} = \frac{ {(3 + \sqrt{7} )}^{2} }{4} \\ = \frac{9 + 7 + 6 \sqrt{7} }{4} = \frac{16 + 6 \sqrt{7} }{4} \\ 4 {x}^{2} + \frac{1}{ {x}^{2} } = 4( \frac{16 + 6 \sqrt{7} )}{4} ) + \frac{4}{16 + 6 \sqrt{7} } \\ = 16 + 6 \sqrt{7} + \frac{2(8 - 3 \sqrt{7}) }{(8 + 3 \sqrt{7} )(8 - 3 \sqrt{7}) } \\ = 16 + 6 \sqrt{7} + \frac{2(8 - 3 \sqrt{7}) }{64 - 63} \\ = 16 + 6 \sqrt{7} + 16 - 6 \sqrt{7} \\ = 16 + 16 \\ = 32$

Answer 2

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