SOLUTION: Solve the following problem: The sum of the squares of two consecutive positve even integers is 340. Find the integers.

Question 170625This question is from textbook Algebra structure and method book one
: Solve the following problem: The sum of the squares of two consecutive positve even integers is 340. Find the integers. This question is from textbook Algebra structure and method book one

Found 2 solutions by Alan3354, Mathtut:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve the following problem: The sum of the squares of two consecutive positve even integers is 340. Find the integers.
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x^2 + (x+2)^2 = 340
x^2 + x^2 + 4x +4 = 340
2x^2 + 4x + 4 = 340
x^2 + 2x -168 = 0
(x-12)*(x+14) = 0
x = 12
x = -14
It's 12 and 14, since it said positive.
12*12 + 14*14 = 340, so it's correct.
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
two consecutive positive even integers we will call a and a+2
:
distribute
:
combine a write as a quadratic
:
divide by 2
:

throw out the negative value since we are looking for positive
so the integers are

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=676 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 12, -14. Here's your graph:

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