First slide

Permutations

Question

The number of ordered pairs of integers $(x, y)$ satisfying the equation $x^{2} + 6 x + y^{2} = 4$ is

Moderate

A

2
B

4
C

6
D

8

Solution

$\begin{array}{l} x^{2} + 6 x + y^{2} = 4 \Rightarrow (x + 3)^{2} + y^{2} = 13 \\ \Rightarrow (x + 3, y) = (\pm 3, \pm 2) or (\pm 2, \pm 3) \\ \Rightarrow x = 0, y = \pm 2, x = - 6, y = \pm 2 \\ x = - 1, y = \pm 3, x = - 5, y = \pm 3 \end{array}$

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