If a + b + c = 0, then the value of a³ + b³ + c³ is?

Solution (By Examveda Team)

$$\eqalign{ & a + b + c = 0 \cr & {\text{Let, }}{a^3} + {b^3} + {c^3} = T \cr} $$
$$ \Rightarrow {a^3} + {b^3} + {c^3} - 3abc = \frac{1}{2}\left( {a + b + c} \right)$$      $$\left[ {{{\left( {a - b} \right)}^2} + {{\left( {b - c} \right)}^2} + {{\left( {c - a} \right)}^2}} \right]$$
$$ \Rightarrow {a^3} + {b^3} + {c^3} - 3abc = \left( 0 \right)$$     $$\left[ {{{\left( {a - b} \right)}^2} + {{\left( {b - c} \right)}^2} + {{\left( {c - a} \right)}^2}} \right]$$
$$\eqalign{ & \Rightarrow {a^3} + {b^3} + {c^3} - 3abc = 0 \cr & \Rightarrow {a^3} + {b^3} + {c^3} = 3abc \cr} $$