How to prove that $|bc| \le \frac{3 \sqrt{3} }{16}$?
134912
List of interesting math podcasts?
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
129171
Prove that $1+\frac{1}{3}+\frac{1\cdot 3}{3\cdot 6}+\frac{1\cdot 3\cdot 5}{3\cdot 6 \cdot 9}+.........=\sqrt{3}$
50266
In the following figure prove that: $AK||BC$
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
8027
How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?
87303
Show that $\frac{a}{c} + \frac{b}{d} +\frac{c}{a} + \frac{d}{b}\le-12$
150565
Prove $(a+b)^\frac{1}{n} \le a^\frac{1}{n} + b^\frac{1}{n}$
154716
Prove $\frac{1}{a^3+b^3+abc}+\frac{1}{a^3+c^3+abc}+\frac{1}{b^3+c^3+abc} \leq \frac{1}{abc}$
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
66082
Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
56101
Prove the inequality $\frac{a}{c+a-b}+\frac{b}{a+b-c}+\frac{c}{b+c-a}\ge{3}$
34081
Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
30385
Proving that $\frac{e^x + e^{-x}}2 \le e^{x^2/2}$
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$