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Problem 17 - Entrance Test

If x + y = 12 and xy = 32, find the value of x^3 + y^3.

Correct: A

We know the identity x^3 + y^3 = (x + y)^3 - 3xy(x + y). Given x + y = 12 and xy = 32. Substitute these values into the identity: x^3 + y^3 = (12)^3 - 3(32)(12) = 1728 - (96)(12) = 1728 - 1152 = 576.