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

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) (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

From here, distribute

Then, distribute some more...

Subtract (6X+6)

Then, use the quadratic formula to find your two X's

Do the appropriate multiplication

Keep simplifying
or
So the answer is either or

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:

Next, try -1, 0, 1:

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

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