Prove the following inequality for any positive real numbers x,y,z
112969
Show that $ab + bc + ac \ge a\sqrt{bc} + b\sqrt{ac} + c\sqrt{ab}$
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
56391
Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$
73807
Prove positive definiteness
122156
An inequality concerning three positive numbers
88956
For any three vectors $x,y,z\in\mathbb{R}^d$, we have $ \|y-z\|\cdot\|x\|\leq\|x-y\|\cdot\|z\|+\|z-x\|\cdot\|y\|$
101362
Let a,b,c be positive real number, proof.
139711
prove this inequality with $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$
157733
Are positive real numbers $x,y$ allowed to be taken out during this proof?
20626
Prove that $x^y < y^x$
99820
symetric inequality for a rational function of three variables
156669
Trying to prove a simple (?) inequality
31295
$x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)
143968
Proving this inequality by mathematical induction
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
98002
Let $x$ be a positive real number. Inequality problem with $\pi$ and $x$ terms.
131596
Symmetric Inequality in $\mathbb{R}$