SOLUTION: Find two consecutive positive integers such that the square of the first decreased by 25 equals three times the second.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Find two consecutive positive integers such that the square of the first decreased by 25 equals three times the second.      Log On


   

Question 165000: Find two consecutive positive integers such that the square of the first decreased by 25 equals three times the second.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = first consecutive positive integer
then
x+1 = second consecutive positive integer
.
x^2 - 25 = 3(x+1)
x^2 - 25 = 3x+3
x^2 - 3 - 28 = 0
.
Factoring:
(x-7)(x+4) = 0
therefore,
x = {-4, 7}
.
Since we looking for POSITIVE integers then the solution MUST be:
7 and 8