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The numbers a, $b, c$ satisfy $a + b + c = 10$ and $ab + b c + c a = 31$ . Find $a^{3} + b^{3} + c^{3} - 3 ab c$ .

Competition practiceAlgebra

A70
B380
C690
D100

Step-by-Step Solution

a^{2} + b^{2} + c^{2} = 100 - 62 = 38. S o a^{3} + b^{3} + c^{3} - 3 ab c = (a + b + c) (a^{2} + b^{2} + c^{2} - ab - b c - c a) = 10 (38 - 31) = 70

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Answer: A) 70

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