1

Part of 2019 Bosnia and Herzegovina Junior BMO TST

Problems(1)

Bosnia and Herzegovina JBMO TST 2019 Q1

Source: https://artofproblemsolving.com/community/c6h1870126p12682434

x,y,z

be real numbers (

\frac{x^2-yz}{x(1-yz)}=\frac{y^2-xz}{y(1-xz)}

y\ne z

x\ne z

) different from

0

\frac{x^2-yz}{x(1-yz)}=\frac{y^2-xz}{y(1-xz)}

, prove that the following relation holds:

x+y+z=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}.