Inequality. $3(x^2+xy+y^2)(y^2+yz+z^2)(z^2+zx+x^2)\geq (x+y+z)^2(xy+yz+zx)^2$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
140299
Inequality based on triangle: $\frac{3}{2}\le\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$
12837
Inequality with condition $x^2+y^2+z^2=1$.
62462
Problem with inequality: $ \left| \sqrt{2}-\frac{p}{q} \right| > \frac{1}{3q^2}$
79491
Inequality $(a+b)^2 + (a+b+4c)^2\ge \frac{kabc}{a+b+c}$ for $a,b,c \in\mathbb{R}$
99820
symetric inequality for a rational function of three variables
89799
Knowing that for any set of real numbers $x,y,z$, such that $x+y+z = 1$ the inequality $x^2+y^2+z^2 \ge \frac{1}{3}$ holds.
51769
If $x,y,z\in[-1,1]$ and $1+2xyz\geq x^2+y^2+z^2$, then can we infer $1+2(xyz)^n\geq x^{2n}+y^{2n}+z^{2n}$?
103947
Inequality : $\sum_{k=1}^n x_k\cdot \sum_{k=1}^n \frac{1}{x_k} \geq n^2$
117046
Show that $\frac{a^2}{\sqrt{(1+a^3)(1+b^3)}}+\frac{b^2}{\sqrt{(1+b^3)(1+c^3)}}+\frac{c^2}{\sqrt{(1+c^3)(1+a^3)}} \geq \frac{4}{3}$
72081
$\forall x,y>0, x^x+y^y \geq x^y + y^x$
8207
Can I prove this inequality algebraically?
26876
How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$?
56391
Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
126557
Proving the inequality $\sum_{\text{cyc}} \frac{a}{a^2+b^3+c^3}\le\frac1{5abc}$
95643
Proving $\sum_{cyc} \sqrt{a^2+ab+b^2}\geq\sqrt 3$ when $a+b+c=3$