Question

if a=(3+√7)/2,then find the value of a^2+(1/a^2)
if simplified
${a}^{2} + \frac{1}{a{}^{2} } \: \: if \: a \: = \frac{3 + \sqrt{7} }{2}$
so,pls anaswer fast​

Answer 1

Answer:

$given \\ a = \frac{3 + \sqrt{7} }{2} \\therefore \: \frac{1}{a} = \frac{2}{3 + \sqrt{7} } \\ = \frac{2(3 - \sqrt{7})}{(3 + \sqrt{7})(3 - \sqrt{7}) } \\ = \frac{2(3 - \sqrt{7})}{ {3}^{2} - ( { \sqrt{7} )}^{2} } \\ = \frac{2(3 - \sqrt{7})}{9 - 7 } \\ = \frac{2(3 - \sqrt{7}) }{2} \\ = 3 - \sqrt{7}$