5

Part of 2003 Purple Comet Problems

Problems(1)

Problem 5, Fall 2003 , MS and HS

Source:

a

b

c

be nonzero real numbers such that

a + \frac{1}{b} = 5

b + \frac{1}{c} = 12

c + \frac{1}{a} = 13

abc + \frac{1}{abc}