Question

If a= 4-√5, find the value of a^2+1/a^2

Answer 1

a = 4-√5

=> 1/a = 1/(4-√5)
=> 1/a = 1/(4-√5)×(4+√5)/(4+√5)
(rationalizing the denominator)


=> 1/a = (4+√5)/(4²-(√5)²)
=> 1/a = (4+√5)/16-5
=> 1/a = (4+√5)/11

(a+1/a)² = a²+1/a²+2

=> (4-√5+(4+√5)/11)² = a²+1/a²+2

=> [(11(4-√5)+4+√5)/11] -2 = a²+1/a2

=> (44-11√5+4+√5)/11 - 2 = a²+1/a²

=> (48-10√5)/11 - 2 = a²+1/a²

=> (48-10√5-22)/11 = a²+1/a²

=> (26-10√5)/11 = a²+1/a²



hope this helps