Show that if $x$ and $y$ are nonnegative reals, then $\frac{x + y}{ 2} ≥ \sqrt{xy}$
1305
Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
45918
Inequality: $x^2+y^2+xy\ge 0$
12484
Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.
104498
Show that $x^3y^3(x^3+y^3) \leq 2$
20593
Show that if $a \neq b$ and a and b are positive then $\frac{a}{b}+\frac{b}{a}$ is never an integer
103851
Show that $\frac{xy}{z} + \frac{xz}{y} + \frac{yz}{x} \geq x+y+z $ by considering homogeneity
84987
Two paths that show that $\frac{x-y}{x^2 + y^2}$ has no limit when $(x,y) \rightarrow (0,0)$
14952
Prove: $\frac{x}{\sqrt{y}}+\frac{y}{\sqrt{x}}\geq \sqrt{x}+\sqrt{y}$
31295
$x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
69082
Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
31544
How to prove that this polynomial is larger than another for positive reals?
8027
How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$