Another AIME problem

Algebra Level 3

\[\begin{cases} xyz=1 \\ x+ \dfrac{1}{z}= 5 \\ y+\dfrac{1}{x} = 29 \end{cases} \]

Suppose that \(x\), \(y\) and \(z\) are three positive numbers that satisfy the system of equations above. Then \(z+ \dfrac{1}{y}= \dfrac{m}{n}\), where \(m\) and \(n\) are relatively prime positive integers. Find \(m+n \).

×

Problem Loading...

Note Loading...

Set Loading...