Question

If x+y+z=0 then what is the value of x^3+y^3+z^3?

Answer 1

If x+y+z=0 then x^3+y^3+z^3=3xyz

Prove: x^3+y^3+z^3-3xyz= (x+y+z)(x^2+y^2+z^2-xy-yz-xz)

LHS

(0)(“)

=0

X^3+y^3+z^3-3xyz=0

X^3+y^3+z^3=3 xyz

All the best!

Answer 2

Heya mate,Here is ur answer

x+y+z=0

x+y=-z

Cubing both the sides

(x+y)^3= (-z)^3

x^3 +y^3 +3xy(x+y) = -z^3

But x+y=-z

x^3 +y^3 +3xy(-z)=-z^3

x^3+y^3-3xyz=-z^3

x^3 +y^3 +z^3 = 3xyz

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