perplexus.info :: Just Math : Derive a formula

Derive a formula (Posted on 2023-07-27)

Given
a+b+c=0 and abc=4

Evaluate S=a^3+b^3+c^3

See The Solution Submitted by Ady TZIDON

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Algebraic Solution

Comment 3 of 3 |

(a+b+c)^3 = a^3 + b^3 + c^3

+ 3(a^2(b+c) + b^2(a+c) + c^2(a+b))

+ 6 abc

Given a+b+c = 0 and abc = 4, we have

0 = a^3 + b^3 + c^3

+ 3(a^2(-a) + b^2(-b) + c^2(-c))

+ 6 * 4

0 = a^3 + b^3 + c^3

- 3(a^3 + b^3 + c^3)

+ 24

2(a^3 + b^3 + c^3) = 24

a^3 + b^3 + c^3 = 12

Posted by Larry on 2023-07-27 09:23:56

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