How to prove using AM-GM $ \frac{4}{abcd} \ge \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} $
41558
Prove that $\frac4{abcd} \geq \frac a b + \frac bc + \frac cd +\frac d a$
5694
How to prove $a^2 + b^2 + c^2 \ge ab + bc + ca$?
87303
Show that $\frac{a}{c} + \frac{b}{d} +\frac{c}{a} + \frac{d}{b}\le-12$
152053
Proof that $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geq a+b+c$
132098
Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.
66089
Using AM-GM to prove $\lim_{p\to 0}$ of the $p$-mean is equal to the GM.
44705
Prove that $\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$
90670
Prove $a^ab^bc^c\ge (abc)^{\frac{a+b+c}3}$ for positive numbers.
136994
Proving :$\frac{1}{2ab^2+1}+\frac{1}{2bc^2+1}+\frac{1}{2ca^2+1}\ge1$
60673
To prove $\sum_{cyc}\frac{1}{a^3+b^3+abc} \le \frac{1}{abc}$
2019
Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$
146885
How prove this inequality $\frac{a-b}{b+c}+\frac{b-c}{c+d}+\frac{c-d}{d+e}+\frac{d-e}{e+a}+\frac{e-a}{a+b}\ge 0$
14763
How to prove $\frac{1}{4}(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{d}+\frac{d^2}{a})\ge \sqrt[4]{\frac{a^4+b^4+c^4+d^4}{4}}$
15116
Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$
66742
Proving the AM-GM Inequality with Lagrange Multipliers
18606
How prove $\frac{a^2}{a+2b^2}+\frac{b^2}{b+2c^2}+\frac{c^2}{c+2a^2}\ge 1$
19896
Prove $\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\geq \frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}$