thay xyz=2017 vaf 2017=xyz a đc :
\(\frac{xyz.x}{xy+xyz.x+xyz}+\frac{y}{yz+y+xyz}+\frac{z}{xz+z+1}\)=\(\frac{xyz.x}{xy.\left(xz+z+1\right)}+\frac{y}{y.\left(xz+z+1\right)}+\frac{z}{xz+z+1}\)
=\(\frac{xz}{xz+z+1}+\frac{1}{xz+z+1}+\frac{z}{xz+z+1}=\frac{xz+z+1}{xz+z+1}=1\)
a) CMR nếu \(\frac{x^2-yz}{x\left(1-yz\right)}=\frac{y^2-xz}{y\left(1-zx\right)}\)với x khác y , xyz khác 0 , yz khác 1 , xz khác 1 m thì xy+xz+yz= xyz(x+y+z)
:b) Cho a, b , c là các số thực khác 0 và thỏa mãn :
\(\hept{\begin{cases}a^2\left(b+c\right)+b^2\left(c+a\right)+c^2\left(a+b\right)+2abc=0\\a^{2017}+b^{2017}+c^{2017}=1\end{cases}}\)
Tính giá trị của biểu thức P= \(\frac{1}{a^{2017}}+\frac{1}{b^{2017}}+\frac{1}{c^{2017}}\)
Cho xyz = 1. Tính B = \(\frac{x}{xy+x+1}+\frac{y}{yz+y+1}+\frac{z}{xz+z+1}\)
cho xyz=2006 . chung minh rang \(\frac{2006x}{xy+2006x+2006}+\frac{y}{yz+y+2006}+\frac{z}{xz+z+1}=1\)
cho xyz=2018
tính \(\frac{2018x}{xy+2018x+2018}+\frac{y}{yz+y+2018}+\frac{z}{xz+z+1}\)
Cho xyz=2011
Chứng minh rằng \(\frac{2011x}{xy+2011x+2011}+\frac{y}{yz+y+2011}+\frac{z}{xz+z+1}=1\)
Cho xyz=1
Tính A=\(\frac{x}{-xy+x+1}-\frac{y}{yz-y+1}+\frac{z}{xz+z-1}\)
\(Cho\left(x+y+z\right)\left(xy+yz+xz\right)=xyz\)
\(CMR:x^{2017}+y^{2017}+z^{2017}=\left(x+y+z\right)^{2017}\)
Cho xyz = 2006
Cmr: \(\frac{2006}{xy+2006x+2006}+\frac{y}{yz+y+2006}+\frac{z}{xz+z+1}=1\)
cho xyz=1. tính giá trị biểu thức: S= \(\frac{x}{xy+x+1}+\frac{y}{yz+y+1}+\frac{z}{xz+z+1}\)