Question

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

Answer 1

Recall the formula

 ${\displaystyle a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)}$

When (a + b + c) = 0, we have

 ${\displaystyle a^3+b^3+c^3-3abc=(a^2+b^2+c^2-ab-bc-ca)}$

= 0

${\displaystyle a^3+b^3+c^3-3abc-0}$

⇒ ${\displaystyle a^3+b^3+c^3=3abc}$