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== | ||
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~Someonenumber011 | ~Someonenumber011 | ||
+ | == See also == | ||
+ | |||
+ | {{AHSME box|year=1976|num-b=26|num-a=28}} | ||
+ | {{MAA Notice}} | ||
+ | [[Category:AHSME]][[Category:AHSME Problems]] |
Revision as of 13:57, 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
See also
1976 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.