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Find the two consecutive positive integers whose product is 506.

Solution:

Let x be the first integer.

Then x+1 is the next integer.

The product is 506

x(x+1) = 506

x2 + x = 506

x2 + x - 506 = 0

$$x_1 = \frac{-1+\sqrt{1+4(1)(506)}}{2(1)} = 22$$