What is (x^2 - y^2) equal to ?
For the next two (02) items that follow : Let x = \frac{\sqrt{6} + \sqrt{5}}{\sqrt{6} - \sqrt{5}} and y = \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} + \sqrt{5}}
- A. 22\sqrt{30}
- B. 44\sqrt{30}
- C. 66\sqrt{30}
- D. 88\sqrt{30} ✓
Correct Answer: D. 88\sqrt{30}
Explanation
Rationalizing x and y yields x = (\sqrt{6}+\sqrt{5})^2 = 11+2\sqrt{30} and y = (\sqrt{6}-\sqrt{5})^2 = 11-2\sqrt{30}. Thus x+y = 22 and x-y = 4\sqrt{30}. Therefore, x^2 - y^2 = (x+y)(x-y) = 22 \times 4\sqrt{30} = 88\sqrt{30}.
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