1991 APMO Problems/Problem 3
Problem
Let ,
,
,
,
,
,
,
be positive real numbers such that
. Show that
Solution
By Cauchy-Schwarz, , so
\sum a_i=\sum b_i$.
Let ,
,
,
,
,
,
,
be positive real numbers such that
. Show that
By Cauchy-Schwarz, , so
\sum a_i=\sum b_i$.
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