SOLUTION: 1. Jason says that "the sum of the squares of three consecutive integers is 112." Is this possible? If so, find the value of the integers. If not, explain mathematically. I don

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: 1. Jason says that "the sum of the squares of three consecutive integers is 112." Is this possible? If so, find the value of the integers. If not, explain mathematically. I don      Log On


   

Question 872800: 1. Jason says that "the sum of the squares of three consecutive integers is 112." Is this possible? If so, find the value of the integers. If not, explain mathematically.
I don't understand how I would set up the problem.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + (x+1)^2 + (x+2)^2 = 112
x^2 +x^2+2x+1 + x^2+4x+4 = 112
3x^2 + 6x - 107 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B6x%2B-107+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A3%2A-107=1320.

Discriminant d=1320 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+1320+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+1320+%29%29%2F2%5C3+=+5.05530070819498
x%5B2%5D+=+%28-%286%29-sqrt%28+1320+%29%29%2F2%5C3+=+-7.05530070819498

Quadratic expression 3x%5E2%2B6x%2B-107 can be factored:
3x%5E2%2B6x%2B-107+=+3%28x-5.05530070819498%29%2A%28x--7.05530070819498%29
Again, the answer is: 5.05530070819498, -7.05530070819498. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B6%2Ax%2B-107+%29