Answer:
8 and 9
Step-by-step explanation:
Let these two consecutive positive numbers be x and x + 1
so... x^2 + (x + 1)^2 = 145
x^2 + x^2 + 2x + 1 = 145
2x^2 + 2x + 1 = 145
2x^2 + 2x = 144
2*(x^2 + x) = 144
(x^2 + x) = 72
x^2 + x - 72 = 0
Use the Diamond method for factoring.
-72 = 9 * -8 and 9 + (-8) = 1
x^2 + x - 72 = (x - 8)*(x + 9) = 0
so x = 8 or x = -9, but x > 0 so only x = 8
