New posts in Contest Math

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

The $2019$th strictly positive integer $n$ such that $\binom{2n}{n}$ is not divisible by $5$

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

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

Finding the value of $ax^4+by^4$

Prove that $\angle AEF =90^\circ$ given a square $ABCD$

Eliminating $x$, $y$, $z$ from $\frac{x^2-xy-xz}{a}=\frac{y^2-yx-yz}{b}=\frac{z^2-zx-zy}{c}$ and $ax+by+cz=0$

Looking for different approach to find $\left(x_1+\frac1{x_1}\right)\left(x_2+\frac1{x_2}\right)\left(x_3+\frac1{x_3}\right)$

Explain the solution to USAMO $1991/\rm P3$

USA MO 1980's inequality