SOLUTION: find 3 consecutive integers such that the product of the 2 larger integers is 50 more than 5 times the smallest integer.

Question 599933: find 3 consecutive integers such that the product of the 2 larger integers is 50 more than 5 times the smallest integer.
Answer by Nihal@SriLanka(22) (Show Source): You can put this solution on YOUR website!
let's assume the integers are x, x+1 and x+2 respectively.

We are given that (x+1)(x+2) = 50 + 5x

We proceed to solve this equation as follows
(x+1)(x+2) = 50 + 5x
i.e. x^2 + 3x + 2 = 50 + 5x
i.e. x^2 - 2x + 48 = 0
i.e. (x - 8)(x - 6)= 0
i.e. x = 8 or -6

Hence the required numbers are 8,9 and 10 or -6,-5 and -4 counting negative integers as well.
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