Prove the following inequality for all real numbers a,b,c,d
56166
Prove that $\frac{a}{b+2c+3d}+\frac{b}{c+2d+3a}+\frac{c}{d+2a+3b}+\frac{d}{a+2b+3c} \geq \frac{2}{3}.$
122156
An inequality concerning three positive numbers
126032
Proving a certain inequality
148451
Polynomial inequality proof
149287
Prove that $A,B>0$ and $A_{ij}0$
71299
Prove that $\frac{a}{b} < \frac{a+c}{b+d} <\frac{ c}{d}$
120390
An inequality involving 4 real or complex numbers
137791
Proving inequality $\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq \sqrt{3 \left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)}$
29198
How to prove the following inequality $|\prod_{i=1}^{i=n}a_i-\prod_{i=1}^{i=n}b_i| < n\delta$?
3030
Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$
52157
Prove that $d(n)\leq 2\sqrt{n}$
57096
Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$
47072
Proving the inequality $\frac{9}4\ + \frac{3abc}4\ \ge ab+bc+ca$
6613
AM-GM inequality: $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{d} + \frac{d^2}{a} \geq a + b + c + d$
87303
Show that $\frac{a}{c} + \frac{b}{d} +\frac{c}{a} + \frac{d}{b}\le-12$
134535
Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$
143968
Proving this inequality by mathematical induction