Question 139
Let $x$, $y$, $z$ be three real numbers such that
- $y$, $x$, $z$ form a harmonic sequence; and
- $3 x y$, $5 y z$, $7 z x$ form a geometric sequence.
The numerical value of $\frac{y}{z} + \frac{z}{y}$ can be expressed in the form $p/q$, where $p$ and $q$ are relatively prime positive integers. What is $p+q$?
- $y$, $x$, $z$ form a harmonic sequence; and
- $3 x y$, $5 y z$, $7 z x$ form a geometric sequence.
The numerical value of $\frac{y}{z} + \frac{z}{y}$ can be expressed in the form $p/q$, where $p$ and $q$ are relatively prime positive integers. What is $p+q$?