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Math Help - Consecutive integers

  1. #1
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    Consecutive integers

    There is a question that asks: Find three consecutive integers such that the sum of their squares is 149?

    I chose to represent the consecutive integers as x, x+1, x+2. Another person chose to represent it as x-1, x, x+1. It then becomes:

    x^2 + (x+1)^2 + (x+2)^2 = 149

    or

    (x-1)^2 + (x)^2 + (X+2)^2 = 149

    The second method gave 7 or -7 as an answer which does give 149. However, when I plug 7 into my method, it does not work. Why? Is it because my method will find a different 3 consecutive integer that will work?
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  2. #2
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    Quote Originally Posted by Masterthief1324 View Post
    There is a question that asks: Find three consecutive integers such that the sum of their squares is 149?

    I chose to represent the consecutive integers as x, x+1, x+2. Another person chose to represent it as x-1, x, x+1. It then becomes:

    x^2 + (x+1)^2 + (x+2)^2 = 149

    or

    (x-1)^2 + (x)^2 + (X+2)^2 = 149

    The second method gave 7 or -7 as an answer which does give 149. However, when I plug 7 into my method, it does not work. Why? Is it because my method will find a different 3 consecutive integer that will work?
    Well yeah.

    He found, 6,7,8. If you plug in 7 you get 7,8,9

    Try plugging in x=6 into yours


    Consider you could also solve... (x-2)^2 + (x-1)^2 + x^2 = 149.

    If you set x=7 you get 5^2 + 6^2 + 7^2.

    But consider you could also solve... x^2 + (x+1)^2 + (x+2)^2 = 149

    If you set x=7 you get 7^2 + 8^2 + 9^2.


    Just to make sense of this... x=7 is not a solution as you can interpret it in a few ways.

    The solution is 6^2 + 7^2 + 8^2 = 149.


    Hence 'x' could be 6,7 or 8 depending on how you set it up.
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  3. #3
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    Quote Originally Posted by Masterthief1324 View Post

    (x-1)^2 + (x)^2 + (X+2)^2 = 149
    These are not consecutive. Did you solve this one separately? You should not use the answer for the first to confirm the second.
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  4. #4
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    Quote Originally Posted by Masterthief1324 View Post
    Another person chose to represent it as x-1, x, x+1. It then becomes:
    (x-1)^2 + (x)^2 + (X+2)^2 = 149
    Correct your typo: (x+2) should be (x+1) ; then you'll be ok
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