Cho a+b+c=3 và a,b,c>0 . CMR \(\sqrt{a+3b}+\sqrt{b+3c}+\sqrt{c+3a}\le6\)

Cho x,y,z>0 thoả mãn: x+y+z+xy+yz+zx=6. Cmr: x²+y²+z²\(\ge3\)

Cho a,b,c>0 thoả mãn : a+b+c=3. CMR: \(\frac{1}{a^2+1}+\frac{1}{b^2+1}+\frac{1}{c^2+1}\ge\frac{3}{2}\)

Tim GTLN: P= \(\frac{\sqrt{x-2019}}{2019x}+\frac{\sqrt{y-2020}}{2020y}\)

Cho \(x\ge3,y\ge2,z\ge1.CMR\)

\(\frac{xy\sqrt{z-1}+xz\sqrt{y-2}+yz\sqrt{x-3}}{xyz}\le\frac{1}{2}+\frac{\sqrt{2}}{4}+\frac{\sqrt{3}}{6}\)