If x + y + z = 6 and xy + yz + zx = 10, then the value of x3 + y3 + z3 - 3xyz is?

Answer: Option A

$$\begin{array}{rl}& \text{Given}\\ & x+y+z=6\\ & xy+yz+zx=10\\ & \text{To find }{x}^3+y^3+z^3-3xyz\text{ = ?}\\ & \Rightarrow \text{ Using formula,}\end{array}$$
  $$\Rightarrow {\left(x+y+z\right)}^2=$$   $$x^2+$$ $$y^2+$$ $$z^2+$$ $$2\left(xy+yz+zx\right)$$
$$\begin{array}{rl}& \Rightarrow 6^2=x^2+y^2+z^2+2\times 10\\ & \Rightarrow 36=x^2+y^2+z^2+20\\ & \Rightarrow x^2+y^2+z^2=16\end{array}$$
  $$\Rightarrow x^2+y^2+z^2-3xyz=$$     $$\left(x+y+z\right)$$  $$\left(x^2+y^2+z^2-xy-yz-zx\right)$$
$$\begin{array}{rl}& \Rightarrow x^2+y^2+z^2-3xyz=6\left[16-10\right]\\ & \Rightarrow x^2+y^2+z^2-3xyz=6\times 6\\ & \Rightarrow x^2+y^2+z^2-3xyz=36\end{array}$$