One positive interger is 1 less than twice another. The sum of their square is 794. Find the intergers.

Let 2x - 1 be the second number   ....then x is the first number....so we have

(2x - 1)² + x² =  794         .... simplify....

4x² - 4x + 1 + x² = 794   rearrange and simplify

5x2 - 4x - 793 = 0     factor

(5x + 61)(x - 13) = 0   Since the integer is positive, x - 13 = 0 →   x = 13

So 2(13) - 1 = 25

So the integers are 13 and 25