SOLUTION: Consecutive integers. I need to find three consecutive integers such that the sum of their squares is 77.

Question 39885: Consecutive integers.
I need to find three consecutive integers such that the sum of their squares is 77.
Answer by vidhyak(98) (Show Source): You can put this solution on YOUR website!
Let the 3 integers be x, x+1, x+2
x^2 + (x+1)^2 + (x+2)^2 = 77
x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 77
3x^2 + 6x + 5 = 77
3x^2 + 6x - 72 = 0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=900 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4, -6. Here's your graph:

Solving you get 4, -6
The 3 integers are 4,5,6 or -6,-5,-4
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