Question

if (x+y+z)=0
then proove that
$( {x}^{3} + {y}^{3} + {z}^{3} ) = 3xyz$

Answer 1

${x}^{3} + {y}^{3} + {z}^{3} = (x + y + z) ( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx)$
So, if (x+y+z) = 0 , then the RHS becomes 0
Since LHS=RHS,
LHS or
${x}^{3} + {y}^{ 3} + {z}^{ 3} = 0$
Hence, Proved