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If a + b + c = 0 and a^3 + b^3 + c^3 = 216, find the value of abc.

 Dec 12, 2019
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If

\(a + b + c = 0 \)

and

\(a^3 + b^3 + c^3 = 216\),

find the value of \(abc\).

 

Formula:  \(\boxed{a^3+b^3+c^3 = 3abc+(a+b+c)(a^2+b^2+c^3-ab-bc-ca)}\)

 

\(\begin{array}{|rcll|} \hline \underbrace{a^3+b^3+c^3}_{=216} &=& 3abc+\underbrace{(a+b+c)}_{=0}(a^2+b^2+c^3-ab-bc-ca) \\\\ 216 &=& 3abc+0 \\ 3abc &=& 216 \quad | \quad : 3 \\ \mathbf{abc} &=&\mathbf{72} \\ \hline \end{array}\)

 

laugh

 Dec 12, 2019

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