Find two consecutive positive integers such the sum of their squares is 145

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