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if x+y+z=0,then x3+y3+z3 is

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if x+y+z=0,then x³+y³⁺z³is

Posted by Ajay Gupta 8 years, 7 months ago

Rashmi Bajpayee 8 years, 7 months ago

Since,

{tex}{x^3} + {y^3} + {z^3} - 3xyz = \left( {x + y + z} \right)\left( {{x^2} + {y^2} + {z^2} - xy - yz - zx} \right){/tex}

Putting x + y + z = 0 [Given]

=> {tex}{x^3} + {y^3} + {z^3} - 3xyz = \left( 0 \right)\left( {{x^2} + {y^2} + {z^2} - xy - yz - zx} \right){/tex}

=> {tex}{x^3} + {y^3} + {z^3} - 3xyz = 0{/tex}

=> {tex}{x^3} + {y^3} + {z^3} = 3xyz{/tex}

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