If x - 3 - 2 = 0 and y - 3 + 2 , then the value of ( x^3 - 20 2 ) - ( y^3 + 2 2 )?

Answer: Option D

$$\begin{array}{rl}& \text{According to the question,}\\ & x=\sqrt{3}+\sqrt{2}\\ & y=\sqrt{3}-\sqrt{2}\\ & \left(x^3-20\sqrt{2}\right)-\left(y^3+2\sqrt{2}\right)\\ & =\left[{\left(\sqrt{3}+\sqrt{2}\right)}^3-20\sqrt{2}-{\left(\sqrt{3}-\sqrt{2}\right)}^3-2\sqrt{2}\right]\end{array}$$
  $$=3\sqrt{3}+2\sqrt{2}+9\sqrt{2}+6\sqrt{3}-$$       $$20\sqrt{2}-$$  $$3\sqrt{3}+$$  $$2\sqrt{2}+$$  $$9\sqrt{2}-$$  $$6\sqrt{3}-$$  $$2\sqrt{2}$$
$$\begin{array}{rl}& =9\sqrt{3}-9\sqrt{2}-9\sqrt{3}+9\sqrt{2}\\ & =0\end{array}$$