The difference of two positive integers is 3 and the sum of their squares is 89. The integers are _____?

{7, 9}

{5, 8}

{4, 8}

None of these

Let's denote the two integers as x and y, where x > y:

Given x - y = 3 and x² + y² = 89.

From x - y = 3, we get x = y + 3.

Substitute x in the second equation:

(y + 3)² + y² = 89

y² + 6y + 9 + y² = 89

2y² + 6y - 80 = 0

y² + 3y - 40 = 0

(y + 8)(y - 5) = 0

y = -8 (not possible since y is positive) or y = 5.

If y = 5, then x = y + 3 = 8.

Check: 8² + 5² = 64 + 25 = 89.

The integers are 8 and 5.