I'm having a hard time figuring out this question,

" There is only one positive number that satisfies the equation

(greek letter phe) - 1 = 1 / (greek letter phe)

Based on this definition, find the value of phe."

Thanks for the help I really appreciate it.

x-1 = 1/x

x^2 - x = 1
x^2 - x - 1 = 0

x = [ 1 +/- sqrt (1+4) ]/2

x = .5 +/- .5 sqrt 5

since it has to be positive
x = .5 + .5 sqrt 5