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Numbers a, $b, c$ satisfy $a + b + c = 6, ab + b c + c a = 11$ and $ab c = 6$ . Find $a^{3} + b^{3} + c^{3}$ .

Competition practiceAlgebra

A36
B198
C54
D18

Step-by-Step Solution

a^{3} + b^{3} + c^{3} = (a + b + c)^{3} - 3 (a + b + c) (ab + b c + c a) + 3 ab c = 216 - 198 + 18 = 36

. (They are 1, 2, 3.)

Answer: A) 36

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