SOLUTION: The sum of the squares of three consecutive positive even integers is 308. Find the integers using a quadratic equation.

Algebra.Com
Question 277506: The sum of the squares of three consecutive positive even integers is 308. Find the integers using a quadratic equation.
Answer by Stitch(470)   (Show Source): You can put this solution on YOUR website!
The equation:
Lets rewrite the equation
Do the multiplication
Simplify
Combine like terms
Subtract 308 from both sides
Notice taht each term is divisible by 3. So factor out a 3
Divide both sides by 3

Now use the quadratic formula
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=400 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8, -12. Here's your graph:


Since the question stated that they were positive integers, 8 is the only answer for X.
So the numbers are: 8, 10, 12
RELATED QUESTIONS

Find three consecutive positive even integers such that the sum of their squares is... (answered by Alan3354)
Solve by using a quadratic equation to find three consecutive integers such that the sum... (answered by htmentor)
the sum of the squares of two consecutive positive even integers is 340. find the... (answered by HyperBrain)
the sum of the squares of two consecutive positive even integers is 340. find the... (answered by bucky)
The sum of the squares of two consecutive even positive integers is 340.Find the... (answered by checkley77)
the sum of the squares of two positive consecutive even integers is 100. Find the... (answered by drk)
the sum of the squares of two consecutive positive even integers is 340. Find the... (answered by harpazo)
The sum of four consecutive even integers is 308 find the four... (answered by Alan3354)
The sum of four consecutive even integers is 308. Write and solve an equation to find... (answered by jim_thompson5910)