Posted by **LP** on Wednesday, December 19, 2012 at 7:39pm.

Find three consecutive odd integers such that the square of the first increased by product of the other two is 224.

- Math -
**Reiny**, Wednesday, December 19, 2012 at 10:00pm
let the middle number be x

then the 1st is x-2

and the 3rd is x+2

(x-2)^2 + x(x+2) = 224

x^2 - 4x + 4 + x^2 + 2x = 224

2x^2 -2x - 220 = 0

x^2 - x - 110 = 0

(x-11)(x+10) = 0

x = 11 or x = -10, but x is to be odd

so

x = 11

and the three numbers are 9, 11, and 13

check:

9^2 + 11(13) = 224 , YEAH!

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