Difference between revisions of "1976 AHSME Problems/Problem 27"
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<cmath>\begin{align*} | <cmath>\begin{align*} | ||
| − | x&=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}\cdot\frac{\sqrt{\sqrt{5} | + | x&=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}\cdot\frac{\sqrt{\sqrt{5}-1}}{\sqrt{\sqrt{5}-1}} |
\end{align*}</cmath> | \end{align*}</cmath> | ||
Revision as of 01:45, 8 September 2021
Contents
Problem
If ![\[N=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}},\]](http://latex.artofproblemsolving.com/f/0/8/f0884a5496b3ee2348e2a6edeacfa5a6879de8f5.png)
then 
equals
Solution 1
Let 
and 
Clearly, 
and 
are both positive.
Note that
from which 
On the other hand, note that
Finally, the answer is 
~Someonenumber011 (Fundamental Logic)
~MRENTHUSIASM (Reconstruction)
Solution 2
Let and Clearly, and are both positive.
Note that
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. 
