1977 USAMO Problems/Problem 5

Problem

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

\[(a \plus{} b \plus{} c \plus{} d \plus{} e)\left(\frac {1}{a} \plus{} \frac {1}{b} \plus{} \frac {1}{c} \plus{} \frac {1}{d} \plus{} \frac {1}{e}\right) \le 25 \plus{} 6\left(\sqrt {\frac {p}{q}} \minus{} \sqrt {\frac {q}{p}}\right)^2\] (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