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

1 Answer
MattyMatty
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).#

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