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 x2
and the 3rd is x+2
(x2)^2 + x(x+2) = 224
x^2  4x + 4 + x^2 + 2x = 224
2x^2 2x  220 = 0
x^2  x  110 = 0
(x11)(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! 
Math  gricelis, Tuesday, March 1, 2016 at 10:03pm
i got this so correct omg im so happy