SOLUTION: The sum of the squares of two consecutive odd numbers is 1154 What are the two numbers????

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The sum of the squares of two consecutive odd numbers is 1154 What are the two numbers????       Log On


   

Question 1116855: The sum of the squares of two consecutive odd numbers is 1154
What are the two numbers????
Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the squares of two consecutive odd numbers is 1154
What are the two numbers????
:
n^2 +(n+2)^2 = 1154
FOIL
n^2 + n^2 + 4n + 4 - 1154 = 0
A quadratic equation
2n^2 + 4n - 1150 = 0
Divide by 2
n^2 + 2n - 575 = 0
Factors to
(n+25)(n-23) = 0
positive solution
n = 23
:
23^2 + 25^2 = 1154

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the squares of two consecutive odd numbers is 1154
What are the two numbers????
---------------
One ? is sufficient.
---
1154/2 = 577
sqrt(577) =~ 24.0208
--> 23 & 25
=====================
If you want to do it the hard way:
(n-1)^2 + (n+1)^2 = 1154
2n^2 + 2 = 1154
n^2 = 576
n = 24
--> 23 & 25