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

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