If (x2+y2+z2)=(xy+yz+zx), what is the value of x3+y3+z3?

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Question

If

(x^{2} + y^{2} + z^{2}) = (x y + y z + z x)

,

what is the value of x^{3} + y^{3} + z^{3}

?

Options:

A . 3xyz

B . −3xyz

C . 2xyz

D . −2xyz

Answer: Option A
:
A
We know that

x^{3} + y^{3} + z^{3} - 3 x y z = (x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x) - - - (1)

According toquestion,

(x^{2} + y^{2} + z^{2}) = (x y + y z + z x)

.

∴

RHS will be zero in equation (1)
So,

x^{3} + y^{3} + z^{3} = 3 x y z

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