Question 126

The value of $$(3+2\sqrt{2})^{-3}+(3-2\sqrt{2})^{-3}$$ is

Solution

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

View More Questions From Algebra

Create a FREE account and get: