Nonosaki Akiho

Cho a,b,c duong. Cmr:

$\frac{a}{\sqrt{a^{2}+b^{2}}}+\frac{b}{\sqrt{b^{2}+c^{2}}}+\frac{c}{\sqrt{c^{2}+a^{2}}}\leq \frac{3}{\sqrt{2}}$

Giai pt:

$x^{2}+\sqrt{x}=5$

Cho a,b,c>0 tm a+b+c=6. Cmr

$\frac{a}{\sqrt{b^{3}+1}}+\frac{b}{\sqrt{c^{3}+1}}+\frac{c}{\sqrt{a^{3}+1}}\leq 2$

giai he pt:

$\left\{\begin{matrix}y^{6}+y^{3}+2x^{2}=\sqrt{xy-x^{2}y^{2}} & \\ 8xy^{3}+2y^{3}+1\geq4x^{2}+2\sqrt{1+(2x+y)^{2}} & \end{matrix}\right.$

$\left\{\begin{matrix} x=\sqrt{y+45}-\sqrt{y+5}& \\ y=\sqrt{x+45}-\sqrt{x+5}& \end{matrix}\right.$