Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 15"
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==Problem== | ==Problem== | ||
− | The expression | + | The expression <math>\frac{1}{2+\sqrt7} + \frac{1}{\sqrt7+\sqrt{10}}+ \frac{1}{\sqrt{10}+\sqrt{13}} + \frac{1}{\sqrt{13}+4}</math> equals |
− | + | <math>\mathrm{(A)}\ \frac{3}{4}\qquad\mathrm{(B)}\ \frac{3}{2}\qquad\mathrm{(C)}\ \frac{2}{5}\qquad\mathrm{(D)}\ \frac{1}{2}\qquad\mathrm{(E)}\ \frac{2}{3}</math> | |
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− | B | ||
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− | C | ||
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− | D | ||
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− | E | ||
==Solution== | ==Solution== |
Latest revision as of 09:29, 27 April 2008
Problem
The expression equals
Solution
Multiply all of the terms by their complex conjugates to simplify:
This telescopes to .
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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 |