Question

solve................... ​

Answer 1

==> 1/a^2 = 1 / {(4 - √15)^2}

Rationalizing the denominator,

==> {(4 + √15 ) / (16-15)}^2 = (4 + √15)^2

= 30 + 8 √15

==> a^2 = (4 - √15)^2

= 30 - 8 √15

Therefore, (a^2) + (1/a^2) = (30 + 8√15)  + (30 - 8√15)

= 30 + 8√15 + 30 - 8 √15

= 60

Hope you found this helpful :)