Prove that $xy+yz+zx \leq x^2+y^2+z^2$
5694
How to prove $a^2 + b^2 + c^2 \ge ab + bc + ca$?
18313
show this inequality with $xy+yz+zx=3$
92692
Prove $3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$
20626
Prove that $x^y < y^x$
83531
Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $
139711
prove this inequality with $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$
49209
Prove $(x+y)(y+z)(x+z)≤\frac8{27}(x+y+z)^3$
152053
Proof that $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geq a+b+c$
111443
Optimization of $2x+3y+z$ under the constraint $x^2+ y^2+ z^2= 1$
152167
Prove that if $x,y,z$ are integers such that $x^2+y^2=z^2$, then $xyz \equiv o \pmod{60}$.
14677
Proving the exponential inequality: $x^y+y^x\gt1$
86211
If $x+y+z \geq xyz$ Prove that $x^2 + y^2 + z^2 \geq xyz$.
106609
Show that $e^{iy} = 1 + iy + \frac{\mu_1 y^2}{2}$ for all $y \in \mathbb{R}$ with $|\mu_1| \leq 1$
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
22528
maximum value of $xy+yz+zx.$ given $x+2y+z=4$
29151
Equation with Vieta Jumping: $(x+y+z)^2=nxyz$.