Question

If $x+y+z=0$
then $x^3+y^3+z^3$=___?

• A. 0
• B. -3xyz
• C. 3xyz
• D. 2xyz

Answer 1

The correct option is C

3xyz

$x^3$+$y^3$+$z^3–3xyz$ = $(x+y+z)(x^2+y^2+z^2-2xy–2yz–2zx)$

If $x+y+z=0$

then $x^3+y^3+z^3–3xyz=0$,

$⟹x^3+y^3+z^3=3xyz$