# math

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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.

• math -

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.

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