Elementary inequality: $x^x+y^y \geq x^y +y^x$?
72081
$\forall x,y>0, x^x+y^y \geq x^y + y^x$
108704
Help with proof of $|x+y| \geq |x|-|y|$
156555
Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
51769
If $x,y,z\in[-1,1]$ and $1+2xyz\geq x^2+y^2+z^2$, then can we infer $1+2(xyz)^n\geq x^{2n}+y^{2n}+z^{2n}$?
124968
How prove this inequality $\sum\limits_{cyc}\frac{x+y}{\sqrt{x^2+xy+y^2+yz}}\ge 2+\sqrt{\frac{xy+yz+xz}{x^2+y^2+z^2}}$
77493
Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
16798
Prove the inequality $n! \geq 2^n$ by induction
14952
Prove: $\frac{x}{\sqrt{y}}+\frac{y}{\sqrt{x}}\geq \sqrt{x}+\sqrt{y}$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
41364
How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
2504
Inequality $\left|\,x_1\,\right|+\left|\,x_2\,\right|+\cdots+\left|\,x_p\,\right|\leq\sqrt{p}\sqrt{x^2_1+x^2_2+\cdots+x^2_p}$
42581
Simple algebra square root inequality
52115
Show that $e^x > 1 + x + x^2/2! + \cdots + x^k/k!$ for $n \geq 0$, $x > 0$ by induction
107601
Use of inequality $1 - \cos (x) \leq x^2 /2$
98921
Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
106934
$x^x=y$. How to solve for $x$?