If a = 9

^{1/3} - 3

^{1/3} + 1,

what is the value of [(4-a)/a]^{6}

We know that x^3 + y^3 = (x+y)(x^2-xy+y^2)

So, for (x,y)=(3^1/3, 1), we have:

4 = a*(3^1/3 + 1)

=> (3^1/3 + 1) = 4/a

=> [(4-a)/a] = 3^1/3

=> [(4-a)/a]^6 = (3^1/3)^6 = 3^2 = 9

*Edited on ***January 19, 2013, 11:17 am**