Difference between revisions of "1976 AHSME Problems/Problem 27"
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We will split this problem into two parts: The fraction on the left and the square root on the right. | We will split this problem into two parts: The fraction on the left and the square root on the right. | ||
| − | Starting with the fraction on the left, begin by squaring the numerator and putting a square root around it. It becomes <math>\frac{\sqrt{(\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2})^2}}{\sqrt{\sqrt{5}+1}}</math> | + | Starting with the fraction on the left, begin by squaring the numerator and putting a square root around it. It becomes |
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| + | <math>\frac{\sqrt{(\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2})^2}}{\sqrt{\sqrt{5}+1}} = \frac{\sqrt{(\sqrt{5}+2)+(\sqrt{5}-2)+2( | ||
| + | \sqrt{(\sqrt{5}+2)(\sqrt{5}-2)}}}{\sqrt{\sqrt{5}+1}}</math> | ||
Revision as of 17:01, 20 March 2020
Problem 27
If 
, then 
equals
Solution
We will split this problem into two parts: The fraction on the left and the square root on the right.
Starting with the fraction on the left, begin by squaring the numerator and putting a square root around it. It becomes
