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Question
If a + b + c = 0, then write the value of a3 + b3 + c3.
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Solution
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 = (a^2 +b^2 +c^2 - ab - bc - ca)`
= 0
`a^3 +b^3 +c^3 - 3abc - 0`
⇒ `a^3 +b^3 +c^3 = 3abc`
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