How to prove $x^2 + y^2 + z^2\geq xy + xz + yz$
139692
Proof of inequality using AM-GM inequality
17100
Prove that $\frac{b^2+c^2}{b+c}+\frac{c^2+a^2}{c+a}+\frac{a^2+b^2}{a+b} \ge a+b+c$
45918
Inequality: $x^2+y^2+xy\ge 0$
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
137522
Hard inequality $ (xy+yz+zx)\left(\frac{1}{(x+y)^2}+\frac{1}{(y+z)^2}+\frac{1}{(z+x)^2}\right)\ge\frac{9}{4} $
135365
If $x, y, z$ are the side lengths of a triangle, prove that $x^2 + y^2 + z^2 < 2(xy + yz + xz)$
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} $
27911
How can I prove that $xy\leq x^2+y^2$?
67666
show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
152053
Proof that $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geq a+b+c$
36507
If $x,y>0$ and $x^2+y^3\ge x^3+y^4$, prove that $x^3+y^3 \le 2$.
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
99676
Prove $\sum{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$
117281
How prove this inequality $x^3y+y^3z+z^3x\ge xyz(x+y+z)$
12837
Inequality with condition $x^2+y^2+z^2=1$.
8027
How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?