if the arithmetic mean of 2 positive numbers (a and b) is 16 and their geometric mean is 12, find the exact value of a^3+b^3.
AM = (a+b)/2
GM = √ab
a+b = 32
ab = 144
(a+b)^2 = (a^2 + b^2 + 2ab)
1024 = a^2 + b^2 + 288
a^2 + b^2 = 736
a^3 + b^3 = (a+b)(a^2 - ab + b^2)
= 32(736 - 144) = 18944
Not bad, for not knowing either a or b.