If a+1/a=√5 than a^5+1/a^5=?

Question

I don't know about that this answer

I do not know what I mean.

Answer 1

Square a+1/a = 5, then a^2+1/a^2+2=5

a^2+1/a^2=3

now multiply a+1/a for both side

a^3+1/a^3+a+1/a=3√5

a^3+1/a^3 +√5 = 3√5

a^3+1/a^3 = 2√5

now (a^2+1/a^2)*(a^3+1/a^3) = (3)*(2√5)

a^5+1/a^5+a+1/a = 6√5. Since a+1/a = √5,

a^5+1/a^5 = 6√5-√5 =5√5

Answer : 5√5