ta có \(\left(x+y+z\right)^2=x^2+y^2+z^2+2\left(xy+yz+xz\right)\)
\(\Rightarrow x^2+y^2+z^2=9\)
áp dung bu nhi a \(2\left(y^2+z^2\right)\ge\left(y+z\right)^2\)
\(\Leftrightarrow2\left(9-x^2\right)\ge\left(5-x\right)^2\)
\(\Leftrightarrow18-2x^2\ge25-10x+x^2\)
\(\Leftrightarrow0< =3x^2-10x+7\)
suy ra 1<=x<=7/3
Cho x, y, z >0 thỏa mãn x + y + z = 1
CMR: \(\sqrt{\dfrac{xy}{xy+z}}+\sqrt{\dfrac{yz}{yz+x}}+\sqrt{\dfrac{zx}{zx+y}}\le\dfrac{3}{2}\)
Cho x,y,z là các số thực dương
CMR: \(\dfrac{1}{x^2+yz}+\dfrac{1}{y^2+zx}+\dfrac{1}{z^2+xy}\le\dfrac{x+y+z}{2xyz}\)
Cho 0≤x, y, z≤1. CMR: \(\frac{x}{1+yz}+\frac{y}{1+zx}+\frac{z}{1+xy}\le2\)
Cho x, y, z >0 thỏa mãn x + y + z= xyz
CMR: \(\dfrac{x}{x^2+yz}+\dfrac{y}{y^2+xz}+\dfrac{z}{z^2+xy}\le\dfrac{\sqrt{3}}{2}\)
cho x,y,z thỏa mãn \(x+y+z\le\dfrac{3}{2}\) . tìm GTNN của \(P=\dfrac{x\left(yz+1\right)^2}{z^2\left(xz+1\right)}+\dfrac{y\left(xz+1\right)^2}{y^2\left(xy+1\right)}+\dfrac{z\left(xy+1\right)^2}{x^2\left(yz+1\right)}\)
Cho x,y,z là ba số dương thỏa mãn x+y+z = 3. CMR:
\(\dfrac{x}{x+\sqrt{3x+yz}}+\dfrac{y}{y+\sqrt{3y+zx}}+\dfrac{z}{z+\sqrt{3z+xy}}\le1\)
cho x,y,z ≠0 và đôi một khác nhau thỏa mãn \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0\). . CMR: \(\left(\dfrac{1}{x^2+2yz}+\dfrac{1}{y^2+2zx}+\dfrac{1}{z^2+2xy}\right)\left(x^{2016}+y^{2017}+z^{2018}\right)=xy+yz+zx\)
cho x,y,z dương thỏa mãn x+y+z=1. CMR:
\(\sqrt{x+yz}+\sqrt{y+zx}+\sqrt{z+xy}\ge1+\sqrt{xy}+\sqrt{yz}+\sqrt{zx}\)
Cho x,y,z > 0 , tm x+y+x=1
CMR \(\sqrt[3]{xy}+\sqrt[3]{yz}+\sqrt[3]{zx}\le\sqrt[3]{3}\)
