Question

Find two positive even consecutive integers such that the square of the smaller integer is 10 more than the larger integer.

Answer 1

Let x be the smaller
x^2 = 10 + (x + 2)
x^2 = x + 12
x^2 - x - 12 = 0
(x - 4)(x + 3) = 0
x = 4 or x = -3
The numbers are 4 and 6.