Question

Suzie is thinking of 2 positive numbers. One of them is 4 more than the other, and the sum of theirs squares is 208. What are the numbers? Just checking my answers, I got 8 and 12.

Answer 1

x and x+4. sum of squares:
2x^2 + 8x + 16 = 208
2x^2 + 8x - 192 = 0
2(x^2 + 4x - 96) = 0
2(x - 8)(x + 12) = 0
roots at x = 8 and x = -12.
throw away the negative root and we get the two integers are 8 and 12.