If $${\text{ }}x - \sqrt 3 - \sqrt 2 = 0$$    and $$y - \sqrt 3 + \sqrt 2 {\text{,}}$$    then the value of $$\left( {{x^3} - 20\sqrt 2 } \right) - $$   $$\left( {{y^3} + 2\sqrt 2 } \right)?$$

Solution (By Examveda Team)

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