Question

Solve question no. 4 ....who will answer first and briefly will marked as brainliest. ....

Answer 1

$a = \frac{3 + \sqrt{5} }{2} \\ {a}^{2} + \frac{1}{ {a}^{2} } = {a}^{2} + \frac{1}{ {a}^{2} } + 2 - 2 \\ \\ = ( {a + \frac{1}{a} )}^{2} - 2 \\ \\ = {( \frac{3 + \sqrt{5} }{2} + \frac{2}{3 + \sqrt{5} } )}^{2} - 2 \\ = ( { \frac{3 + \sqrt{5} }{2} + \frac{2(3 - \sqrt{5}) }{(3 + \sqrt{5})(3 - \sqrt{5} ) } ) }^{2} - 2 \\ = ( { \frac{3 + \sqrt{5} }{2} + \frac{6 - 2 \sqrt{5} }{9 - 5} ) }^{2} - 2 \\ \\ = ( { \frac{6 + 2 \sqrt{5} + 6 - 2 \sqrt{5} }{4} )}^{2} - 2 \\ \\ = ( { \frac{12}{4}) }^{2} - 2 \\ \\ = {3}^{2} - 2 \\ = 9 - 2 \\ = 7 \: \: \: ans$