Answer to January 11, 1999 Problem

Ordered Pairs Problem

Find all ordered pairs of integers which satisfy

x^2 + 4x + y^2 = 9


Solution:

Complete the square:
x^2 + 4x + 4 + y^2 = 9 + 4

(x + 2)^2 + y^2 = 13

The only two squares whose sum is 13 are 4 and 9.
So, (x + 2) = +/- 2 and y = +/-3

or (x + 2) = +/- 3 and y = +/- 2

Hence, the solution is:
(1, 2), (1, -2), (0, 3), (0, -3),
(-4, 3), (-4, -3), (-5, 2), (-5, -2).

Correctly solved by:

No one.