Question

Two integers differ by 12 and the sum of their squares is 74. find the integers.

Answer 1

Let x is the smaller integer.
     x+12 is the larger integer because two integers differ by 12.
The sum of their square means
x² + (x+12)² = 74
x² + x² + 24x + 144 = 74
2x² + 24x + 70 = 0
2(x² + 12x + 35) = 0
2(x+5)(x+7) = 0
x = -5 or - 7
so we have two answer. 
first x = -5 as smaller and 7 as the larger x = -5 + 12 = 7
second x = -7 as smaller and 5 as the larger. x = -7 + 12 = 5