If x - √3 - √2 = 0 and y - √3 + √2, then the value of (x³ - 20√2) - (y³ + 2√2) ?

Explanation:-

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