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If $a + b = 12$ and $a^{2} + b^{2} = 80$ , find $a^{3} + b^{3}$ .

Competition practiceAlgebra

A576
B1152
C640
D432

Step-by-Step Solution

2 ab = 144 - 80 = 64, so ab = 32. a^{3} + b^{3} = 1 2^{3} - 3 \times 32 \times 12 = 1728 - 1152 = 576

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Answer: A) 576

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