Question

If $(x^2+y^2+z^2)=(xy+yz+zx)$, $\text{what is the value of}{x}^3+y^3+z^3$?

• A. 3xyz
• B. -3xyz
• C. 2xyz
• D. -2xyz

Answer 1

The correct option is A

3xyz

We know that

$x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)---\left(1\right)$

According to question, $(x^2+y^2+z^2)=(xy+yz+zx)$.
$\therefore$ RHS will be zero in equation (1)

So,$x^3+y^3+z^3=3xyz$