\(\frac{1}{x}-\frac{1}{y}-\frac{1}{z}=1\Rightarrow\left(\frac{1}{x}-\frac{1}{y}-\frac{1}{z}\right)^2=1\)
=>\(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}-\frac{2}{xy}-\frac{2}{xz}+\frac{2}{yz}=1\)
Ta có:\(-\frac{2}{xy}-\frac{2}{xz}+\frac{2}{yz}=-2\left(\frac{z+y-z}{xyz}\right)=0\)(Do x=y+z=>y+z-x=0)
=>ĐPCM