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Math Help - word problem - quadratics

  1. #1
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    word problem - quadratics

    Aaaalright, apparently I'm supposed to solve this using the quadratic formula (ps: you dont have to run through the steps of the formula with me, i'm good with that part)

    Here is the word problem: The sum of the squares of two consecutive numbers is 481. Find the integers.

    How do I solve this?

    Thank you
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  2. #2
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    Let the smaller integer be x, then the consecutive integer is x+1. The sum of the squares of these numbers is 481, which leads us to the equation x^2+(x+1)^2=481.
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  3. #3
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    But then, won't it end up having a degree of 4? Is that still ok?
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  4. #4
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    Oh, never mind. lol it does work
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  5. #5
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    Quote Originally Posted by cyph1e View Post
    Let the smaller integer be x, then the consecutive integer is x+1. The sum of the squares of these numbers is 481, which leads us to the equation x^2+(x+1)^2=481.
    Quote Originally Posted by dancingqueen9 View Post
    But then, won't it end up having a degree of 4? Is that still ok?
    Just to make sure you understand, let me build on cyph1e's foundation.

    x^2+(x+1)^2=481

    x^2+(x^2 + 2x + 1) = 481

    2x^2 + 2x + 1 =481

    2x^2 + 2x - 480 = 0

    2(x^2 + x - 240) = 0

    2(x + 16)(x - 15) = 0
    Last edited by janvdl; July 13th 2008 at 12:46 PM.
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  6. #6
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    Quote Originally Posted by janvdl View Post
    These numbers are not consecutive, although there squares do add up to 481. Their absolute values are consecutive though. (15 and 16)

    (Unless I did something stupid again... )
    There are two solutions; \left\{(15,16),(-16,-15)\right\}. The quadratic equation gives only the smaller integer x, while the other consecutive integer of x is x+1.
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  7. #7
    Bar0n janvdl's Avatar
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    Quote Originally Posted by cyph1e View Post
    There are two solutions; \left\{(15,16),(-16,-15)\right\}. The quadratic equation gives only the smaller integer x, while the other consecutive integer of x is x+1.
    Ah, of course you are correct! I knew I forgot something simple again.
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