SOLUTION: Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number

Question 321696: Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Three consecutive whole numbers are such that the square of the middle number
is greater than the product of the other two by 1.
Find the middle number:
There is no unique solution
:
let x = the middle number
then
(x-1) = the 1st number
and
(x+1) = the 3rd number
:
x^2 = ((x-1)*(x+1)) + 1
FOIL
x^2 = x^2 - 1 + 1
:
x^2 = x^2
Which means this is true for any 3 consecutive numbers even, -1, 0 +1
:
Try a few like; 142, 143, 144: 143^2 = 20449, 142*144 = 20448

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