February 1, 1999
Problem of the Month

Reciprocal Riddle
from Problem Solving A Handbook for Teachers by Krulik and Rudnik

The sum of two numbers is 2, and the product of these same two numbers is 3.

Determine the sum of their reciprocals.

Solution to the Problem:

The answer is 2 / 3

Let x and y represent the two numbers.   Then

x + y = 2

xy = 3

This yields x = 1 + 1.414 i
and y = 1 - 1.414 i

But there is a more artistic solution:
1/x + 1/y = (x + y) / (xy) = 2 / 3

Correctly solved by:

1. Michael Leatherman

Norfolk, VA

Send any comments or questions to: David Pleacher