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If $a + b + c = 9, ab + b c + c a = 26$ and $ab c = 24$ , find $a^{3} + b^{3} + c^{3}$ .

Competition practiceAlgebra

A171
B72
C99
D27

Step-by-Step Solution

a^{2} + b^{2} + c^{2} = 81 - 52 = 29. a^{3} + b^{3} + c^{3} = 3 ab c + (a + b + c) (a^{2} + b^{2} + c^{2} - ab - b c - c a) = 72 + 9 \times 3 = 99

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Answer: C) 99

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