Cho a,b,c dương tm \(a+b\le c\). Tìm GTNN của \(P=\left(a^4+b^4+c^4\right)\left(\dfrac{1}{4a^4}+\dfrac{1}{4b^4}+\dfrac{1}{c^4}\right)\)

\(P=\dfrac{x\left(4x^2+3\right)+y\left(4y^2+3\right)}{x+y+4xy}\)

Cho a,b,c>0 tm a+b+c=8. C/m\(\dfrac{a^2+2a}{31}+\dfrac{b^2+2b}{13}+\dfrac{c^2+2c}{7}\ge\dfrac{11930}{2821}\)

\(\dfrac{a}{1-a^2}+\dfrac{b}{1-b^2}+\dfrac{c}{1-c^2}\ge\dfrac{3\sqrt{3}}{2}\)

\(\left\{{}\begin{matrix}2y^3+y^2+6y+3=\left(x-x^2+3\right)\left(\sqrt{x}+\sqrt{1-x}\right)^2\\32\left(2xy-2y^3-y\right)^2=\dfrac{1-x}{x^2+x}\end{matrix}\right.\)

Cho x,y,z>0. Tìm max của

\(P=\dfrac{1}{\sqrt{x^2+4y^2+9z^2+1}}-\dfrac{2}{\left(x+1\right)\left(2y+1\right)\left(3z+1\right)}\)

Tìm m để pt sau có nghiệm: \(\sqrt{x-m}+\sqrt{1-x}=3m\)

Giải hpt: \(\left\{{}\begin{matrix}\dfrac{x-y}{1-xy}=\dfrac{5-y}{5y-1}\\\dfrac{x+y}{1+xy}=-\dfrac{x+5}{5x+1}\end{matrix}\right.\)