SOLUTION: the difference between 2 positive integers is 5. if the smaller is added to the square of the larger,the sum is 301, find the integers. please help me and i thank you in advance.

Algebra ->  Equations -> SOLUTION: the difference between 2 positive integers is 5. if the smaller is added to the square of the larger,the sum is 301, find the integers. please help me and i thank you in advance.      Log On


   

Question 866162: the difference between 2 positive integers is 5. if the smaller is added to the square of the larger,the sum is 301, find the integers.
please help me and i thank you in advance.
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the smaller positive integer and
let b = the larger positive integer
Then we have two equations
(1) b - a = 5 and
(2) a + b^2 = 301
Solve (1) for b and substitute it into (2) and get
(3) a + (5 + a)^2 = 301 or
(4) a + 25 + 10a +a^2 - 301 = 0 or
(5) a^2 + 11a - 276 = 0
Use the quadratic equation solution formul
(6) %28-11%2B-sqrt%2811%5E2-4%2A1%2A%28-276%29%29%2F%282%2A1%29%29 and get
(7) a = {-23,12}
We select a = 12, because it must be a positive integer. Using (1) we get
(8) b = 5 + 12 or
(9) b = 17
Check these values using (2).
Is (12 + 17^2 = 301)?
Is (12 + 289 = 301)?
Is (301 = 301)? Yes
Answer: The two positive integers are 12 and 17.
PS a = -23 and b = -18 should also be a solution. Try it in (2).