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Problem 13 - Entrance Test

If x+y=12 and x²+y²=84, then x³+y³=

Correct: A

x³+y³=(x+y)(x²−xy+y²). xy=[(x+y)²−(x²+y²)]/2=[144−84]/2=30. So x³+y³=12×(84−30)=12×54=648.