Question

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

Answer 1

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