Another AIME problem

Algebra Level 3

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

Suppose that xx, yy and zz are three positive numbers that satisfy the system of equations above. Then z+1y=mnz+ \dfrac{1}{y}= \dfrac{m}{n}, where mm and nn are relatively prime positive integers. Find m+nm+n .

×

Problem Loading...

Note Loading...

Set Loading...