Find three consecutive integers such the product of the fi..

[cmdrox]

Find three consecutive integers such the product of the first and third minus the second is 1 more than 10 times the third. Find all possible consecutive integers.

So I have x, x + 1 and x + 2. My equation is:

\(\displaystyle \L x(x + 2) - x + 1 = 10(x + 2) + 1\)

\(\displaystyle \L x^2 + 2x - x + 1 = 10x + 20 + 1\)

\(\displaystyle \L x^2 + x + 1 = 10x + 21\)

\(\displaystyle \L x^2 + x + 1 - 10x - 21\)

\(\displaystyle \L x^2 - 9x -20 = 0\)

How do I finish this up?

I have the answers as 11, 12, 13 or -2, -1, 0, but I don't know how to get there

Thanks.

 

[ilaggoodly]

you made a mistake, try any of the answers in your final equation, and see that they dont fit, the original mistake was x(x+2) -x + 1 where it should actually be x(x+2)-(x+1)

 

[Denis]

Keep it simpler: make the consecutives (x-1), x and (x+1);
easier to multiply (x-1)(x+1) = x^2 - 1