Các câu hỏi tương tự
24 tháng 8 2017 lúc 14:59
cho x,y,z là số thực dương thỏa mãn xy+yz+xz=xyz
cmr \(\frac{xy}{z^3\left(1+x\right)\left(1+y\right)}+\frac{yz}{x^3\left(1+y\right)\left(1+z\right)}+\frac{xz}{y^3\left(1+x\right)\left(1+z\right)}\ge\frac{1}{16}\)
x;y;z>0. CMR: \(\left(1+\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\left(1+\frac{z}{x}\right)\ge2+\frac{2\left(x+y+z\right)}{\sqrt[3]{xyz}}\)
cho xyz=1.CMR
\(\frac{1}{x^3\left(y+z\right)}+\frac{1}{y^3\left(x+z\right)}+\frac{1}{z^3\left(y+z\right)}\ge\frac{3}{2}\)
cho x y z > 0 và xyz=1. Tìm Min của \(P=\frac{x^3}{\left(1+x\right)\left(1+y\right)}+\frac{y^3}{\left(1+y\right)\left(1+z\right)}+\frac{z^3}{\left(1+z\right)\left(1+x\right)}\)
x,y,z>0,xyz=1
P=\(\frac{x^3}{\left(1+z\right)\left(1+y\right)}+\frac{y^3}{\left(1+x\right)\left(1+z\right)}+\frac{z^3}{\left(1+x\right)\left(1+y\right)}\). tìm gtnn của P.
Cho x,y,z dương thỏa mãn xyz=1.CMR :
1) A\(=\frac{1}{x^2+x+1}+\frac{1}{y^2+y+1}+\frac{1}{z^2+z+1}\ge1\)
2) B\(=\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(y+1\right)\left(y+2\right)}+\frac{1}{\left(z+1\right)\left(z+2\right)}\ge\frac{1}{2}\)
Cho x,y,z>0 thỏa mãn xy+yz+xz=xyz. CMR :
\(\frac{xy}{z^3\left(1+x\right)\left(1+y\right)}+\frac{yz}{X^3\left(1+y\right)\left(1+z\right)}+\frac{xz}{y^3\left(1+z\right)\left(1+x\right)}\) lớn hơn hoặc bằng \(\frac{1}{16}\)
Help me ... Plzzz
Cho x y z > 0 và xyz=1.Tìm \(P=\frac{x^3}{\left(1+x^2\right)\left(1+y^2\right)}a+\frac{y^3}{\left(1+y^2\right)\left(1+z^2\right)}+\frac{z^3}{\left(1+z^2\right)\left(1+x^2\right)}\)
Cho x,y,z>0; xyz=1. Tìm Min H=\(\frac{1}{x^3\left(y+z\right)}+\frac{1}{y^3\left(x+z\right)}+\frac{1}{z^3\left(x+y\right)}\)