The maximum of $\frac{1}{(2a+b+c)^2}+\frac{1}{(2b+c+a)^2}+\frac{1}{(2c+a+b)^2}$
101362
Let a,b,c be positive real number, proof.
29424
Maximum value of $\sin A+\sin B+\sin C$?
122300
Maximizing a quadratic function subject to $\| x \|_2 \le 1$
57096
Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$
19896
Prove $\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\geq \frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}$
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
4099
Inequality $\sum\limits_{cyc}\frac{a^3}{13a^2+5b^2}\geq\frac{a+b+c}{18}$
56796
Maximum of $x^3+y^3+z^3$ with $x+y+z=3$
134535
Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
145152
How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
14763
How to prove $\frac{1}{4}(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{d}+\frac{d^2}{a})\ge \sqrt[4]{\frac{a^4+b^4+c^4+d^4}{4}}$
20055
Find minimum value of $\sum \frac{\sqrt{a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}$
3030
Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$
148744
Prove that $(\frac{bc+ac+ab}{a+b+c})^{a+b+c} \ge \sqrt{(bc)^a(ac)^b(ab)^c}$