SOLUTION: Solve the following problems by defining the variable, writing a quadratic equation, solving it and then providing a written conclusion. - The sum of the squares of two consecu

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the following problems by defining the variable, writing a quadratic equation, solving it and then providing a written conclusion. - The sum of the squares of two consecu      Log On


   

Question 247740: Solve the following problems by defining the variable, writing a quadratic equation, solving it and then providing a written conclusion.
- The sum of the squares of two consecutive even numbers is 1460. Find the numbers.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the squares of two consecutive even numbers is 1460. Find the numbers.
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1st even: 2x
2nd even: 2x+2
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(2x)^2 + (2x+2)^2 = 1460
4x^2 + 4x^2 + 8x + 4 = 1460
8x^2 + 8x -1456 = 0
x^2 + x - 182 = 0
(x-13)(x+14) = 0
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x = 13
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1st: 2x = 26
2nd: 28
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Cheers,
Stan H.