Исбот кунед, ки

\(\frac{1}{1+x+xy}+\frac{1}{1+y+yz}+\frac{1}{1+z+zx}=1\), агар x, y, z=1

\(x\cdot y\cdot z=1\)

\(\frac{1}{1+x+xy}+\frac{1}{1+y+yz}+\frac{1}{1+z+zx}=\)

\(=\frac{1}{1+x+xy}+\frac{x}{x(1+y+yz)}+\frac{xy}{xy(1+z+zx)}=\)

\(=\frac{1}{1+x+xy}+\frac{x}{x+xy+xyz}+\frac{xy}{xy+xyz+x^2yz}=\)

\(=\frac{1}{1+x+xy}+\frac{x}{x+xy+1}+\frac{xy}{xy+1+x\cdot1}=\)

\(=\frac{1}{1+x+xy}+\frac{x}{1+x+xy}+\frac{xy}{1+x+xy}=\)

\(=\frac{1+x+xy}{1+x+xy}=1\)

\(\frac{1}{1+x+xy}+\frac{1}{1+y+yz}+\frac{1}{1+z+zx}=1\)

Исбот шуд