Prove That$\frac{xy}{x^5+y^5+xy}+\frac{yz}{z^5+y^5+yz}+\frac{xz}{z^5+x^5+zx}\le 1$
131596
Symmetric Inequality in $\mathbb{R}$
133382
Proof that $a+b+\frac{1}{1+\sqrt{ab}}\geq\frac{5}{2}$
39082
Proving $x^\alpha-\alpha x \le 1- \alpha $
89728
Prove that $1<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}$
33240
$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 $, prove $ab + bc + ca \le 3$
126959
Prove $ \frac{1}{x+1} \le \ln(1+\frac{1}{x}) \le \frac{1}{x}$ with usage of the definition of a logarithmic function
52800
Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
71299
Prove that $\frac{a}{b} < \frac{a+c}{b+d} <\frac{ c}{d}$
86211
If $x+y+z \geq xyz$ Prove that $x^2 + y^2 + z^2 \geq xyz$.
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
48394
Proving bessel identity $[J_0(x)]^2 + 2[J_1(x)]^2 + 2[J_2(x)]^2 + \cdots = 1$ and $|J_0(x)|\le 1$
14952
Prove: $\frac{x}{\sqrt{y}}+\frac{y}{\sqrt{x}}\geq \sqrt{x}+\sqrt{y}$
148744
Prove that $(\frac{bc+ac+ab}{a+b+c})^{a+b+c} \ge \sqrt{(bc)^a(ac)^b(ab)^c}$
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 $
82961
Show that $\left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right|$.