Các câu hỏi tương tự
Cho x, y, z > 0. CMR :
\(\left(xyz+1\right)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)+\frac{x}{z}+\frac{z}{y}+\frac{y}{x}\ge x+y+z+6\)
Cho x,y,z>0,x+y+z=1.CMR
\(\frac{\sqrt{x}}{1-x}+\frac{\sqrt{y}}{1-y}+\frac{\sqrt{z}}{1-z}\ge\frac{3\sqrt{3}}{2}\)
Cho x;y;z >0 thỏa mãn x+y+z=1. CMR:
\(\frac{1}{x+y}+\frac{1}{y+z}+\frac{1}{z+x}\le\frac{\left(x\sqrt{x}+y\sqrt{y}+z\sqrt{z}\right)\sqrt{xyz}+6\left(x^4+y^4+z^4\right)}{2xyz}\)
cho x,y,z >0 va x+y+z=3 Cm \(\frac{^{x^2}}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y}\ge\frac{3}{2}\)
cho x,y,z>0 va xyz \(\ge\)1 ,tim min
\(x^3+y^3+z^3+\frac{2z}{x+y}+\frac{2x}{y+z}+\frac{2y}{z+x}\)
Cho x,y,z>0, xyz=1
CMR :
\(\frac{x^2}{1+y}+\frac{y^2}{1+z}+\frac{z^2}{1+x}\ge\frac{3}{2}\)
Cho x>0,y>0,z>0, xyz=1
Tìm GTNN
\(P=\frac{x^2\left(y+z\right)}{y\sqrt{y}+2z\sqrt{z}}+\frac{y^2\left(x+z\right)}{z\sqrt{z}+2x\sqrt{x}}+\frac{z^2\left(x+y\right)}{x\sqrt{x}+2y\sqrt{y}}.\)
Cho x, y, z >0 thỏa x + y + z >= 3. Chứng minh rằng : \(\frac{x^2}{x+\sqrt{yz}}+\frac{y^2}{y+\sqrt{xz}}+\frac{z^2}{z+\sqrt{xy}}\ge\frac{3}{2}\)
Cho 3 số dương x,y,z thỏa mãn \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\), Chứng minh rằng:
\(\sqrt{x+yz}+\sqrt{y+zx}+\sqrt{z+xy}\ge\sqrt{xyz}+\sqrt{x}+\sqrt{y}+\sqrt{z}\)