SOLUTION: given 3 consecutive positive integers, it turns out that the difference between the square of the largest number and the square of the smallest number is 12 less than the square of

Question 305106: given 3 consecutive positive integers, it turns out that the difference between the square of the largest number and the square of the smallest number is 12 less than the square of the middle number. what is the sum of the 3 numbers?
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
given 3 consecutive positive integers, it turns out that the difference between the square of the largest number and the square of the smallest number is 12 less than the square of the middle number. what is the sum of the 3 numbers?
Let x be the samllest of the three consecutive integers. Then the other two are x+1 and x+2. We have then:
(x+2)^ - x^2 = (x+1)^2 - 12
x^2 + 4x + 4 - x^2 = x^2 + 2x + 1 - 12
4x + 4 = x^2 + 2x - 11
x^2 - 2x - 15 = 0
(x-5)*(x+3) = 0
x = 5 or x = -3.
Since the integers are positive x must be 5.
The other two integers are x+1 = 6 and x+2 = 7.

RELATED QUESTIONS
given two consecutive positive even integers, it turns out that the square of the larger... (answered by hkwu)

there are 3 consecutive positive odd integers. the difference between the squares of... (answered by checkley79)

There are three consecutive positive integers such that the sum of square of first and... (answered by Edwin McCravy)

find 3 consecutive even integers so that so that difference between the largest and... (answered by Alan3354)

The sum of three consecutive integers equals the difference between 5 times the smallest... (answered by josmiceli)

Given three consecutive integers, what is the difference between the average of their... (answered by spacesurfer)

The difference between the squares of two consecutive positive integers is 15. Find the... (answered by ReadingBoosters)

find three consecutive positive integers, such that the square of the smallest exceeds... (answered by mananth)

Four consecutive even integers have a sum of 508. Find the difference between the largest (answered by macston)