Question

If a + b + c = 0, then write the value of a³ + b³ + c³.

Answer 1

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`