If a + b + c = 0, then write the value of a^3 + b^3 + c^3. - Vidyadip

Question

If $a + b + c = 0$, then write the value of $a^3 + b^3 + c^3.$

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Answer

Recall the formula
$a^3 + b^3 + c^3 - 3abc$ =$(a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$
When, $(a + b + c) = 0,$ we have
$a^3 + b^3 + c^3 - 3abc = 0$.$(a^2 + b^2 + c^2 - ab - bc - ca)$
$= 0$
$a^3 + b^3 + c^3 - 3abc = 0$
$\Rightarrow a^3 + b^3 + c^3 = 3abc$

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