Các câu hỏi tương tự
Cho x , y, z > 0 thoa man: \(x+y+z=\sqrt{x}+\sqrt{y}+\sqrt{z}=2\)
Tính: \(\frac{\sqrt{x}}{1+x}+\frac{\sqrt{y}}{1+y}+\frac{\sqrt{z}}{1+z}\)
cho x,y,z >0. CMR
\(\frac{x}{\sqrt{x}+\sqrt{y}}+\frac{y}{\sqrt{y}+\sqrt{z}}+\frac{z}{\sqrt{x}+\sqrt{z}}=\frac{y}{\sqrt{x}+\sqrt{y}}+\frac{z}{\sqrt{y}+\sqrt{z}}+\frac{x}{\sqrt{x}+\sqrt{z}}\)
10 tik nha !!!!!!!!
Cho x, y, z > 0 và khác nhau đôi một. Tính: \(P=\frac{x}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}-\sqrt{z}\right)}+\frac{y}{\left(\sqrt{y}-\sqrt{z}\right)\left(\sqrt{y}-\sqrt{x}\right)}+\frac{z}{\left(\sqrt{z}-\sqrt{x}\right)\left(\sqrt{z}-\sqrt{y}\right)}\)
Cho x,y,z thỏa mãn \(\frac{x\sqrt{x}}{x+\sqrt{xy}+y}\)+\(\frac{y\sqrt{y}}{y+\sqrt{yz}+z}\)+\(\frac{z\sqrt{z}}{z+\sqrt{zx}+x}\)=1006
Tính giá trị biểu thức M=\(\frac{x\sqrt{x}+y\sqrt{y}}{x+\sqrt{xy}+y}\)+\(\frac{y\sqrt{y}+z\sqrt{z}}{y+\sqrt{yz}+z}\)+\(\frac{z\sqrt{z}+x\sqrt{x}}{z+\sqrt{zx}+x}\)
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 mãn xyz=1. Tìm min \(P=\frac{x^2\left(y+z\right)}{y\sqrt{y}+2z\sqrt{z}}+\frac{y^2\left(z+x\right)}{z\sqrt{z}+2x\sqrt{x}}+\frac{z^2\left(x+y\right)}{x\sqrt{x}+2y\sqrt{y}}\)
Cho x>0, y>0,z>0,xyz=1. CMR \(P=\frac{x^2\left(y+z\right)}{y\sqrt{y}+2z\sqrt{z}}+\frac{y^2\left(z+x\right)}{z\sqrt{z}+2x\sqrt{x}}+\frac{z^2\left(x+y\right)}{x\sqrt{x}+2y\sqrt{y}}\) lớn hơn hoặc bằng 2
Cho x,y,z là các số dương. Chứng minh rằng:
\(\frac{1}{\sqrt{x}+3\sqrt{y}}+\frac{1}{\sqrt{y}+3\sqrt{z}}+\frac{1}{\sqrt{z}+3\sqrt{x}}\ge\frac{1}{\sqrt{x}+2\sqrt{y}+\sqrt{z}}+\frac{1}{\sqrt{y}+2\sqrt{z}+\sqrt{x}}+\frac{1}{\sqrt{z}+2\sqrt{x}+\sqrt{y}}\)
cho x, y, z>0 tm \(\hept{\begin{cases}\sqrt{x}+\sqrt{y}+\sqrt{z}=2\\x+y+z=2\end{cases}}\)
tính A=\(\sqrt{\left(1+x\right)\left(1+y\right)\left(1+z\right)}\left(\frac{\sqrt{x}}{x+1}+\frac{\sqrt{y}}{y+1}+\frac{\sqrt{z}}{z+1}\right)\)