1977 USAMO Problems/Problem 5

Problem

If are positive numbers bounded by and , i.e, if they lie in , prove that

\[(a+b +c +d +e)\left(\frac{1}{a} +\frac {1}{b} +\frac{1}{c} + \frac{1}{d} +\frac{1}{e}\right) \le 25 + 6\left(\sqrt{\frac {p}{q}} \minus{} \sqrt {\frac{q}{p}}\right)^2\] (Error compiling LaTeX. Unknown error_msg)

and determine when there is equality.

Solution

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See Also

1977 USAMO (Problems • Resources)
Preceded by Problem 4	Followed by Last Question
1 • 2 • 3 • 4 • 5
All USAMO Problems and Solutions