SOLUTION: Find three consecutive integers such that two times the sum of all three is 3 times the product of the larger two.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find three consecutive integers such that two times the sum of all three is 3 times the product of the larger two.      Log On


   

Question 857368: Find three consecutive integers such that two times the sum of all three is 3 times the product of the larger two.
Answer by ben720(159) About Me  (Show Source):
You can put this solution on YOUR website!


For three consecutive integers,
Let X = 1st
X+1 = 2nd
X+2 = 3rd
Therefore, the sum of the three is X+(X+1)+(X+2), or 3X+3 total.
For the equation, twice the sum is 3 times the product of the larger two, or
2%283X%2B3%29=3%28X%2B1%29%28X%2B2%29
From here, distribute
6X%2B6=%283X%2B3%29%28X%2B2%29
Then, distribute some more...
6X%2B6=3X%5E2%2B9X%2B6
Subtract (6X+6)
0=3X%5E2%2B3X%2B0
Then, use the quadratic formula to find your two X's
X=%28-3%2B-sqrt%283%5E2-4%2A3%2A0%29%29%2F%282%2A3%29
Do the appropriate multiplication
X=%28-3%2B-sqrt%289-0%29%29%2F%286%29
Keep simplifying
X=%28-3%2B3%29%2F6orX=%28-3-3%29%2F6
So the answer is eitherX=%28-3%2B3%29%2F6=0 or X=%28-3-3%29%2F6=-6%2F6=-1.

And so, the two answers for X are 0 and -1. The second is X + 1, third is X + 2.

Your 2 answers are 0, 1, 2 or -1, 0, 1.

To check, plug each of them in:
2%280%2B1%2B2%29=3%281%2A2%29
2%283%29=3%282%29
6=6
Next, try -1, 0, 1:
2%28-1%2B0%2B1%29=3%280%2A1%29
2%280%29=3%280%29
0=0


Your final, checked answers are 0, 1, and 2; or -1, 0, and 1.