Difference between revisions of "1976 AHSME Problems/Problem 27"
MRENTHUSIASM (talk | contribs) (Centered the important equation: https://files.eric.ed.gov/fulltext/ED239856.pdf Also, I am thinking of making the solution clearer using algebra.) |
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==Solution== | ==Solution== | ||
| + | Let <math>x=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}</math> and <math>y=\sqrt{3-2\sqrt{2}}.</math> Note that | ||
| + | <cmath>\begin{align*} | ||
| + | x^2&=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}} | ||
| + | \end{align*}</cmath> | ||
~Someonenumber011 (Solution) | ~Someonenumber011 (Solution) | ||
| Line 18: | Line 22: | ||
{{AHSME box|year=1976|num-b=26|num-a=28}} | {{AHSME box|year=1976|num-b=26|num-a=28}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
| − | [[Category:AHSME]][[Category:AHSME Problems]] | + | [[Category:AHSME]] |
| + | [[Category:AHSME Problems]] | ||
Revision as of 01:52, 8 September 2021
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
Let 
and 
Note that
~Someonenumber011 (Solution)
~MRENTHUSIASM (Revision)
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. 
