Question

if a=(3+√7)/2, then find the value of a²+1/a²

Answer 1

This answer is not simplified completely.

Answer 2

a = (3 + √7)/2

1/a = 2/( 3 + √7)
=2(3 - √7)/( 3 + √7)(3 -√7)
=2(3 - √7)/(3² -√7²)
=2(3 -√7)/2
=(3 - √7)

now,
a² + 1/a² = (a + 1/a)² -2a.1/a
=(a +1/a)² -2
={ (3 + √7)/2 + (3 - √7)}² -2
={ (3 +√7 +6 -2√7)/4 - 2
={( 9 -√7)² - 8}/4