# Questions tagged [inequality]

Questions on proving, manipulating and applying inequalities.

19,208 questions
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### Techniques for upper bounding square of sum of square roots?

Say I have $x_1,...,x_n$ such that $0 \leq x_i \leq 1$ for all $i \in n$ and $\sum_{i=1}^n x_i = 1$. Let $\epsilon > 0$ be some small number. Let $y_1,...,y_n$ be $\epsilon$-close approximations of ...
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### Hermite - Hadamard inequality [on hold]

What is the geometric meaning of Hermite - Hadamard inequality? I.e. $$f(\frac{a+b}{2})\leq \frac{1}{b-a}\int_{a}^{b} f(x)dx \leq \frac{f(a)+f(b)}{2}.$$ Thank you for your help.
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### Inequality with absolute value function inside absolute value - $||x-2|-3|<4.$ [on hold]

Help me solving this. $||x-2|-3|<4.$ Find all values of x satisfying this.
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### A short problem in geometry 😊 [on hold]

Given an acute triangle $\triangle ABC$. The altitude $AH$ is equal to the median $BM$. Prove: $∠B<60^∘$
In $\Delta ABC$ find the maximum of the value $$\sin{A}+\dfrac{\sqrt{10}}{2}\sin{B}-\sqrt{5}\sin{C}$$