huya1k43pbc

Tìm tất cả hàm f:R->R thỏa mãn: $f(x+f(xy))=f(x)+xf(y) \forall x,y\in R$ (AMM problem)

$$$\left\{\begin{matrix} 2x^2-3xy-2y^2+x+3y-1=\sqrt{x+y+1}-\sqrt{2x-y+2} & \\ 3x^2+9x-6y-4x\sqrt{x-1}-4y\sqrt{x^2+5}=0 & \end{matrix}\right.$$$

$$$\left\{\begin{matrix} 2x^2-3xy-2y^2+x+3y-1=\sqrt{x+y+1}-\sqrt{2x-y+2} & \\ 3x^2+9x-6y-4x\sqrt{x-1}-4y\sqrt{x^2+5}=0 & \end{matrix}\right.$$$

Cho $a,b,c>0;a+b+c=1.CMR \sum \frac{ab}{\sqrt{c}+\sqrt{3}}\leq \frac{1}{4\sqrt{3}}$

Cho $a,b,c>0.CMR: a^3+b^3+c^3+3abc\geq 2\sqrt[3]{abc}(a^2+b^2+c^2)$