अगर $x=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ और $y=\frac{\sqrt{3}+\sqrt{2 }}{\sqrt{3}-\sqrt{2}}$, तो $x^{3}+y^{3}$ का मूल्य है:

$k=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}=\frac{(\sqrt{3}-\sqrt{2})(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}$

$=\frac{(\sqrt{3}-\sqrt{2})^{2}}{3-2}=3+2-2 \sqrt{3} \cdot \sqrt{2}$

$\therefore x+y=5-2 \sqrt{6}+5+2 \sqrt{6}=10$

$x y=(5-2 \sqrt{6})(5+2 \sqrt{6})=25-24=1$

∴ x³ + y³ = (x + y)³ – 3xy (x + y) = (10)³ – 3(10)

= 1000 – 30 = 970