I have reached the following inequality while solving a physics problem and was wondering if this is true.
Let $d\geq 2$ be an integer, and let $0 Any other method to solve this? Maybe it is not true?
Prove $(x-a)^{d/2} + (x+a)^{d/2}\geq 2x^{d/2}$ for $x\geq a$
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inequality
1 Answers
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The function $f(x)=x^{d/2}$ is convex. Now you can apply Jensen's inequality.
$$\frac{f(x-a)+f(x+a)}2\ge f\left(\frac{(x-a)+(x+a)}2\right)$$
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0nice1 man, +1 for sure. – 2017-01-14
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1@A.Molendijk "man" is pretty presumptuous. – 2017-01-14
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0I'm a man, after all, so no problem :) – 2017-01-14