Giải hpt \(\left\{{}\begin{matrix}\sqrt{y+3x}+\sqrt{2x+7y}=\sqrt{5x-y}+3\sqrt{x}\\x-4-\sqrt{y-2}=\sqrt{x^3-10x^2+33x-34}-\sqrt{y^3-9y^2+24y-16}\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x^2+y^2=1\\\left|5x+3y-3\right|-\left|3x+y-3\right|=2\left|x+y\right|\end{matrix}\right.\)

Cho a,b,c là 3 số thực dương t/m ab+bc+ca=1. Tìm min

\(M=\dfrac{1}{4a^2-bc+1}+\dfrac{1}{4b^2-ca+1}+\dfrac{1}{4c^2-ab+1}\)

Giải hpt: \(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{y}=2\\\sqrt{x+3}+\sqrt{y+3}=4\end{matrix}\right.\)

Giai pt \(\left(x+5\right)\sqrt{x+1}+1=\sqrt[3]{3x+4}\)

Giai pt: \(\left\{{}\begin{matrix}\left(\dfrac{x}{y}+\dfrac{y}{x}\right)\left(x+y\right)=15\\\left(\dfrac{x^2}{y^2}+\dfrac{y^2}{x^2}\right)\left(x^2+y^2\right)=85\end{matrix}\right.\)

Cho x,y,z>0 và x+y+z=3

C/m\(\dfrac{x+1}{x^2+1}+\dfrac{y+1}{y^2+1}+\dfrac{z+1}{z^2+1}\ge3\)

Cho x,y,z>0 tm\(xy+yz+zx\ge3\). C/m

\(\dfrac{x^3}{\sqrt{y^2+3}}+\dfrac{y^3}{\sqrt{z^2+3}}+\dfrac{z^3}{\sqrt{x^2+3}}\ge\dfrac{1}{2}\)

Cho x,y,z>0 t/m \(xy+yz+zx\ge3\). C/m

\(\dfrac{1}{\sqrt{x+3y}}+\dfrac{1}{\sqrt{y+3z}}+\dfrac{1}{\sqrt{z+3x}}\ge3\)