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Suppose that for some a,b,c we have a+b+c = 6, ab+ac+bc = 5 and abc = 12. What is a^3+b^3+c^3?

 Dec 9, 2021
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Oh, so convenient! (a^3+b^3+c^3) - (a+b+c)^3 = -3(a+b)(b+c)(a+c).

How convenient! (a+b)(b+c)(a+c) + abc = (a+b+c)(ab+ac+bc).

With these elusive factoring tricks down, we substitute numbers.

(a^3+b^3+c^3) - 216 = -3(30 - 12) = -54

216-54 = 162.

 Dec 9, 2021

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