Question

If x + y + z = 0, then find the value of x3 + y3 +z3.

Answer 1

hope this answer helps you

Answer 2

Answer:

$x^3\ +\ y^3\ +\ z^3\ =\ 3xyz.$

Step-by-step explanation:

Given,

$x\ +\ y\ +\ z\ =\ 0$

We know that , in the algebra,

Hence the formula is,

$\therefore x^3\ +\ y^3\ +\ z^3\ -\ 3xyz\ =\ \dfrac{1}{2}(x\ +\ y\ +\ z)[(x\ -\ y)^2\ +\  (y\ -\ z)^2\ +\ (z\ -\ x)^2$

By substituting the value of $(x\ +\ y\ +\ z)\ =\ 0$ the right hand side of the above expression becomes zero. Hence the expression becomes,

$\therfore x^3\ +\ y^3\ +\ z^3\ -\ 3xyz\ =\ 0\\\Rightarrow x^3\ +\ y^3\ +\ z^3\ =\ 3xyz$

Hence the required value is 3xyz.