Difference between revisions of "1976 AHSME Problems/Problem 27"
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| + | ==Problem== | ||
| + | If <math>N=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}</math>, then <math>N</math> equals | ||
| + | |||
| + | <math>\textbf{(A) }1\qquad \textbf{(B) }2\sqrt{2}-1\qquad \textbf{(C) }\frac{\sqrt{5}}{2}\qquad \textbf{(D) }\sqrt{\frac{5}{2}}\qquad \textbf{(E) }\text{none of these}</math> | ||
==Solution== | ==Solution== | ||
Revision as of 12:56, 20 June 2021
Problem
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
.
Now for the right side.
Putting it all together gives:
~Someonenumber011
