The value of $$(3+2\sqrt{2})^{-3}+(3-2\sqrt{2})^{-3}$$ is
Expression : $$(3+2\sqrt{2})^{-3}+(3-2\sqrt{2})^{-3}$$
= $$\frac{1}{(3 + 2\sqrt{2})^3} + \frac{1}{(3 - 2\sqrt{2})^3}$$
= $$\frac{1}{(27+16\sqrt{2}+54\sqrt{2}+72)} + \frac{1}{(27-16\sqrt{2}-54\sqrt{2}+72)}$$
= $$\frac{1}{99+70\sqrt{2}} + \frac{1}{99-70\sqrt{2}}$$
= $$\frac{99 - 70\sqrt{2} + 99 + 70\sqrt{2}}{9801 - 9800}$$
= 99+99 = 198
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