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. |