Recent content by max2

Thank But I don't have imagine with my problem

simple, i love inequality!(h)

Given that the equation $ax^3-x^2+ax-b=0$, ($a\neq 0,\,b\neq 0$) has three positive real roots. Determine the greatest value of the following expression: $$P=\frac{11a^2-3\sqrt3ab-\frac{1}{3}}{9b-10\left ( \sqrt3a-1 \right )}$$

Let sharp triangle ABC inscribed circle $(O;R)$ and $H$ is orthocenter of triangle ABC. circle $(E;r)$ tangent to $HB$, $HC$ and tangent to in circle $(O;R)$. Prove that: midpoint of $HE$ is center of the circle inscribed the triangle $HBC$