cho a,b,c>0. CMR: \(\frac{1}{a\sqrt{a+b}}+\frac{1}{b\sqrt{b+c}}+\frac{1}{c\sqrt{c+a}}\ge\frac{3}{\sqrt{2abc}}\)

cho a,b,c>0. CMR: \(\frac{a^2-bc}{a+b}+\frac{b^2-ca}{b+c}+\frac{c^2-ab}{c+a}\ge0\)

Cho \(\left\{{}\begin{matrix}a,b,c>0\\a^2+b^2+c^2=1\end{matrix}\right.\). CMR:\(\frac{1}{1-ab}+\frac{1}{1-bc}+\frac{1}{1-ca}\le\frac{9}{2}\)

cho a,b,c>0. CMR:\(\frac{\left(a+b\right)^2}{a^2+b^2+2c^2}+\frac{\left(b+c\right)^2}{b^2+c^2+2a^2}+\frac{\left(c+a\right)^2}{c^2+a^2+2b^2}\le3\)

cho \(\left\{{}\begin{matrix}a,b,c>0\\a+b+c=1\end{matrix}\right.\). chứng minh:\(2\left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)\ge\frac{1+a}{1-a}+\frac{1+b}{1-b}+\frac{1+c}{1-c}\)

\(\frac{3}{x^2-x+1}+\frac{11}{x^2+x+2}=\frac{54}{x^2+5x+4}\)

\(\frac{3}{x^2+3x+2}+\frac{2}{x^2-x+3}=\frac{14}{x^2+11x}\)

\(-2x^2+5+\left(x-5\right)\sqrt{x-1}=0\)

tìm tất cả các giá trị của tham số m để phương trình sau có nghiệm dương \(x^4+2x^3+\left(m-1\right)x^2+2x+1=0\).

cho \(x,y\in R\) thỏa mãn \(x+y\ge1\). Tìm min \(A=\left(x^2+2y^2\right)\left(y^2+2x^2\right)-x^2-y^2-2x^2y^2\)