cho x thỏa mãn \(x^2+\left(3-x\right)^2\ge5\) . Tìm GTNN của \(A=x^4+\left(3-x\right)^4+6x^2\left(3-x\right)^2\)

cho x,y,z >0 thỏa mãn \(x+y+z=\frac{3}{2}\)

Tìm GTNN của \(\frac{\sqrt{x^2+xy+y^2}}{4yz+1}+\frac{\sqrt{y^2+yz+z^2}}{4xz+1}+\frac{\sqrt{z^2+xz+x^2}}{4xy+1}\)

cho a,b,c > 0 thỏa mãn a+b+c+ab+bc+ca=6abc

Cmr: \(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\ge3\)

cho a,b,c ∈ [0 ; 1]. Cmr: \(\frac{a}{b+c+1}+\frac{b}{a+c+1}+\frac{c}{a+b+1}+\left(1-a\right)\left(1-b\right)\left(1-c\right)\le1\)

cho a,b,c > 0 thỏa mãn \(2\left(\frac{a}{b}+\frac{b}{a}\right)+c\left(\frac{a}{b^2}+\frac{b}{a^2}\right)=6\)

Tìm GTNN của \(A=\frac{bc}{a\left(2b+c\right)}+\frac{ac}{b\left(2a+c\right)}+\frac{4ab}{c\left(a+b\right)}\)

cho a,b,c > 0 thỏa mãn a+b+c ≤ 2018. Cmr:

\(\frac{5a^3-b^3}{ab+3a^2}+\frac{5b^3-c^3}{bc+3b^3}+\frac{5c^3-a^3}{ca+3c^3}\le2018\)

cho a,b,c > 0 thỏa mãn \(a+b+c\le2\)

Tìm GTNN của \(A=21\left(a^2+b^2+c^2\right)+12\left(a+b+c\right)^2+2015\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)

choa,b,c > 0. Cmr: \(\sqrt{\frac{2}{a}}+\sqrt{\frac{2}{b}}+\sqrt{\frac{2}{c}}\le\sqrt{\frac{a+b}{ab}}+\sqrt{\frac{b+c}{bc}}+\sqrt{\frac{c+a}{ca}}\)

cho x.y.z > 0 thỏa mãn \(x+y+z=\frac{3}{2}\)

Tìm GTNN của \(A=\frac{\sqrt{x^2+xy+y^2}}{4yz+1}+\frac{\sqrt{y^2+yz+z^2}}{4xz+1}+\frac{\sqrt{z^2+xz+x^2}}{4xy+1}\)

cho x,y,z > 0 thỏa mãn \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\)

Cmr: \(\sqrt{x+yz}+\sqrt{y+xz}+\sqrt{z+xy}\ge\sqrt{xyz}+\sqrt{x}+\sqrt{y}+\sqrt{z}\)