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2007 Cyprus MO/Lyceum/Problem 11

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Problem

If $X=\frac{1}{2007 \sqrt{2006}+2006 \sqrt{2007}}$ and $Y=\frac{1}{\sqrt{2006}}-\frac{1}{\sqrt{2007}}$ , which of the following is correct?

$\mathrm{(A) \ } X=2Y\qquad \mathrm{(B) \ } Y=2X\qquad \mathrm{(C) \ } X=Y\qquad \mathrm{(D) \ } X=Y^2\qquad \mathrm{(E) \ } Y...$

Solution

Define $a = 2007,\ b = 2006$ .

$X = \frac{1}{a\sqrt{b} + b\sqrt{a}} \cdot \left(\frac{a\sqrt{b} - b\sqrt{a}}{a\sqrt{b} - b\sqrt{a}}\right) = \frac{a\sqrt{b} ...$

$X=Y\Longrightarrow\mathrm{ C}$

See also

2007 Cyprus MO, Lyceum (Problems)
Preceded by Problem 10	Followed by Problem 12
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

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/2007_Cyprus_MO/Lyceum/Problem_11"

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