$\left \| x+y \right \|^2+\left \| x-y \right \|^2=2\left \| x \right \|^2+2\left \| y \right \|^2$
73805
How can we get Pythagoras from the Parallelogram law?
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
145884
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
31317
If we know $x+y+z=1$, $x^2+y^2+z^2=2$, and $x^3+y^3+z^3=3$, how to find $x^4+y^4+z^4$?
49211
Solving $f(x+y) = f(x)f(y)f(xy)$
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
7775
Show that $|x-y|\leq |x|+|y|$.
115176
Can we say that $\left(a+b\right)^{\alpha}>a^{\alpha}+b^{\alpha}$ for all $a,b>0$ and $\alpha>1$?
49296
Prove $|(1+|u|^2)v-(1+|v|^2)u|>|u\bar{v}-\bar{u}v|$
49999
Express $y$ from $\ln(x)+3\ln(y) = y$
104498
Show that $x^3y^3(x^3+y^3) \leq 2$
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
8027
How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?
135968
Simplify $\left({\sum_{k=1}^{2499}\sqrt{10+{\sqrt{50+\sqrt{k}}}}}\right)\left({\sum_{k=1}^{2499}\sqrt{10-{\sqrt{50+\sqrt{k}}}}}\right)^{-1}$
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
140459
Why is $\left(e^{2\pi i}\right)^i \neq e^{-2 \pi}$?