What is the number of ordered pair of integers (x,y) satisfying the equation x^2 + 6x + y^2 = 4?

1 Answer
Feb 23, 2018

8

Explanation:

"Complete the square for x : "

"(x+3)^2 + y^2 = 13

"As both terms are positive, we know that"

-4 < x+3 < 4
"and"
-4 < y < 4

y = pm 3 => x+3 = pm 2 => x = -5 or -1
y = pm 2 => x+3 = pm 3 => x = -6 or 0
y = pm 1 " and " y = 0, " yield no perfect square"

"So we have 8 solutions : "
(-5, -3), (-5, 3), (-1, -3), (-1, 3),
(-6, -2), (-6, 2), (0, -2), (0, 2).