give a formula 4 finding A,plz.?

Question

(a+1/a)+(a^2+1/a^2)^2+.........+(a^n+1/a^n)^2=A

Answer 1

let x = a+1/a
y = sum (a+1/a)^r = sum x^r

(1-x)(1+x+x^2 + ... +x^r-1) =
(1+x+x^2 + ... +x^(r-1))
- (x+x^2 + .....x^(r-1))-x^r =
1-x^n
so (1+x+x^2 + ... +x^r-1) = = ( 1-x^r)/(1-x)

y = 1/(1-x) = 1/( 1-(a+1/a)) = a/( a-a^2-1)
so (a-a^2-1) = a/y
so a^2 + (1/y -1)a + 1 = 0
which you can solve as quadrative for a as function of y