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The sum of the non-negative real numbers
is 2 and. Find the largest and smallest possible values ofLast edited by tony123 (2007-11-08 06:27:29)
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Use the CauchySchwarz inequality.
Last edited by JaneFairfax (2007-12-18 14:52:42)
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the Cauchy-Schwartz inequality - its everywhere!
A logarithm is just a misspelled algorithm.
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The CauchySchwarz inequality is
Taking
we get
Taking
we get
Since both inequalities have to be satisfied, we take the first one: S ≥ 1. So the minimum value is 1.
Also
To show that this is attainable, take
. So the maximum value of S is 2.Last edited by JaneFairfax (2007-11-08 18:29:03)
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Umm, sorry. The first part of my working is wrong. Ive been trying to find an example for which S = 1, but Ive come to realize that this is impossible.
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