New posts in Inequality

Difference between the maximum and minimum values ​of $a+b$ that satisfy $a+b+\frac{1}{a}+\frac{9}{b}=10, (a,b\in\mathbb{R}^+)$

Prove that $\frac{a^2}{a^2+bc}+\frac{b^2}{b^2+ac}+\frac{c^2}{c^2+ab}<2$

Algebraic inequality $\sum \frac{x^3}{(x+y)(x+z)(x+t)}\geq \frac{1}{2}$

Proving $\sum_{cyc} \frac{a(a^2+2bc)}{b+c}\ge \frac{{(a+b+c)}^2}{2}$

How to prove this lower bound on $\log(1+x)$ for $x \geq 0$? How about $x > -1$?

proving that $\alpha_1+\alpha_2<-3$ which are the negative roots of $f(x)$

Let ABCD be a tetrahedron of volume 1 and M,N,P,Q,R,S on AB,BC,CD,DA,AC,BD s.t. MP,NQ,RS are concurrent. Then the volume of MNRSPQ is less than 1/2.

USA MO 1980's inequality

$\frac 21 \times \frac 43 \times \frac 65 \times \frac 87 \times \cdots \times \frac{9998}{9997} \times \frac {10000}{9999} > 115$

$\frac{2}{3} \cdot \frac{5}{6} \cdot \frac{8}{9} \cdot ... \cdot \frac{995}{996} \cdot \frac{998}{999}$ and $0.1$ which is bigger?