Let x be one of the integers.

Then the other integer then is x+4.

The product of the two is 252 so:

x*(x+4) = 252

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click here to see the quadratic equation solved for x

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x1 = 14

x2 = -18

For x = 14 the second integer is 14 + 4 = 18.

Indeed 14*18 = 252.

For x = -18 the second integer is -18 + 4 = -14.

Indeed (-18)*(-14) = 252.

There are 2 solutions: first solution is the integers are 14 and 18, second solution is the integers are -18 and -14.