Answer to Problem of the Week for 2/01/99

Answer to February 1, 1999 Problem

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: 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

Solution:

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