a and b are positive numbers that satisfy the equation 1/a−1b=1/a+b. Determine the value of a^6/b^6+b^6/a^6.

Answer 1

Solving you would get

b^2 - a^2 = ab -> b/a + a/b = 1,

now let a/b =x,
so x + 1/x = 1 -> x^2-x+1 =0

Solve for x = [1+ root(5)]/2 = a/b