Prove that $||x-y||·||x+y|| < ||x||^2+||y||^2$
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
115583
prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
80009
Prove that $| |a|-|b| | \le |a-b|$
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
109778
Proving $(x-c)|(p(x)-p(c))$
8207
Can I prove this inequality algebraically?
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
20626
Prove that $x^y < y^x$
77026
Proof with inequalities