Question 1047463: Find two consecutive odd integers such that their product is 83
more than 4
times their sum.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
Two consecutive odd integers: n, (n+2)
:
Find two consecutive odd integers such that their product is 83 more than 4 times their sum.
n(n+2) = 83 + 4(n+(n+2))
n^2 + 2n = 83 + 4(2n+2)
n^2 + 2n = 83 + 8n + 8
n^2 + 2n = 8n + 91
Arrange as a quadratic equation
n^2 + 2n - 8n - 91 = 0
n^2 - 6n - 91 = 0
You can use the quadratic formula; a=1; b=-6, c=-91, but this will factor to:
(n-13)(n+7) = 0
Then positive solution
n = 13, 15 are two the integers
:
How about the negative solution? n = -7, -5, see if they work too
-7(-5) = 83 + 4(-12)
35 = 83 - 48, OK also
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