Which of the following is true for all positive real numbers , and ?
Answer and explanation
Correct answer: A.
- Step 1: for positive .
- Step 2: The others fail: fails for ; fails for (equality) and in fact always fails; fails for , (); and in ' with equality only if ' equality holds whenever , not only for .
Answer
.
Why not the others: The correct statement follows from a sum of squares; the others each have an immediate counterexample.
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