cho x,y,z >0

cminh : \(A=\sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{a+c}}+\sqrt{\dfrac{c}{a+b}}>2\)

cho x,y,z nguyen duong thoa man: \(\left\{{}\begin{matrix}\left|x-2y\right|\le\dfrac{1}{\sqrt{x}}\\\left|y-2x\right|\le\dfrac{1}{\sqrt{y}}\end{matrix}\right.\)

tim Max \(A=x^2+2y^2\)

cho a,b,c>0 va abc=1 :  chung minh: 

\(Â=\dfrac{a^5}{b^2\left(c+3\right)}+\dfrac{b^5}{c^2\left(a+3\right)}+\dfrac{c^5}{a^2\left(b+3\right)}\ge\dfrac{3}{4}\)

cho a,b,c>0 va abc=1 :  chung minh: \(A=\dfrac{a^5}{b^2\left(c+3\right)}+\dfrac{b^5}{c^2\left(a+3\right)}+\dfrac{c^5}{a^2\left(b+3\right)}\ge\dfrac{3}{4}\)

ch pt: \(x^3-3\left(m+1\right)x^2+2mx+m+2=0\)

tim m de phuong trinh co 3 nghiem phan biet

thoa man: \(x1+x2=2x3\)

tim m de pt co nghiem duy nhat :\(\left\{{}\begin{matrix}x-2y=\dfrac{my}{x}\\y-2x=\dfrac{mx}{y}\end{matrix}\right.\)