Question

If (a^{​​​​​​2} + b^{​​​​​​2})³ = (a^{​​​​​​3} + b^{​​​​​​3})² then find the value of (a/b) + (b/a)

Answer 1

Expanding both sides of the equation
a^6 + b^6 + 3 a^4 b^2 + 3 a^2 b^4=a^6 + b^6 + 2 a^3 b^3
Cancelling a^6 and b^6
we get 2 a b ( a^2 b^2) = 3 a^2 b^2 ( a^2 + b^2)
Cancelling a^2 b^2 on both side you have a^2 + b^2 / a b = 2/3
Or a/b + b/a = 2/3