# HN_NH

Before age 25, I hope to see an analytical solution of the http://math.stackexchange.com/questions/1775572/olympiad-inequality-sum-cyc-fracx48x35y3-geqslant-fracxyz13.

(BTW, I am 15 as of 2016)

Top Questions

## Olympiad Inequality $\sum\limits_{cyc} \frac{x^4}{8x^3+5y^3} \geqslant \frac{x+y+z}{13}$

asked May 7 '16 at 15:35

## $x,y,z \geqslant 0$, $x+y^2+z^3=1$, prove $x^2y+y^2z+z^2x < \frac12$

asked May 7 '16 at 14:35

## Stronger than Nesbitt inequality

asked Sep 21 '15 at 0:51

## Prove $\left(\frac{a+1}{a+b}\right)^a+\left(\frac{b+1}{b+c}\right)^b+\left(\frac{c+1}{c+a}\right)^c \geqslant 3$

asked Jun 17 '16 at 16:16

## Prove that $\frac{x^x}{x+y}+\frac{y^y}{y+z}+\frac{z^z}{z+x} \geqslant \frac32$

asked May 30 '16 at 12:55

## Prove $a^{ab}b+b^{bc}c+c^{ca}a \geqslant \sqrt[6]{5}$

asked May 6 '16 at 22:41

## Prove $\frac{xy}{5y^3+4}+\frac{yz}{5z^3+4}+\frac{zx}{5x^3+4} \leqslant \frac13$

asked May 31 '16 at 1:03

## $a,b,c >0$, prove $\sqrt[2]{\frac{a}{b+c}}+\sqrt[3]{\frac{b}{c+a}}+\sqrt[4]{\frac{c}{a+b}} \geqslant \frac{7}{12} \cdot2^{\frac67} \cdot 3^{\frac47}$

asked May 8 '16 at 18:44