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Math Help - Is the following result consistent

  1. #1
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    Is the following result consistent

    Is the following result consistent? Explain

    \sum{x^2}=64, \sum{x}=25, n=6
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  2. #2
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    Re: Is the following result consistent

    Quote Originally Posted by Suvadip View Post
    Is the following result consistent? Explain
    \sum{x^2}=64, \sum{x}=25, n=6
    What are the indices? No one can respond without knowing what the sums are.
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  3. #3
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    Re: Is the following result consistent

    It was set in a university exam. I am also confused. We have to search six numbers whose sum is 25 and sum of squares of those six numbers is 64.


    Quote Originally Posted by Plato View Post
    What are the indices? No one can respond without knowing what the sums are.
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  4. #4
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    Re: Is the following result consistent

    Since it includes the information that "n= 6", I would interpret this as summing over 6 terms- and assume that the sums run from 1 to 6:
    \sum_{i= 0}^6 x_i^2= 64 and \sum_{i= 1}^6 x_i= 25

    So the question is "do there exist 6 numbers, that sum to 25, whose squares sum to 64?"

    That is 6 numbers determined by only two equations so it seems to me there ought to be many ways to do that. For example, if we choose to take x_1= 1, x_2= 2, x_3= 3 and x_4= 4 the equations reduce to 1+ 2+ 3+ 4+ x_5+ x_6= 25 or x_5+ x_6= 15 and 1+ 4+ 9+ 16+ x_5^2+ x_6^2= 64 or x_5^2+ x_6^2= 34. Since x_5= 16- x_6 so that x^5^2+ x_6^2= x_6^2- 32x_6+ 64+ x_6^2= 34. x_6^2- 16x_6= -30.

    Was there a requirement that the numbers be integers?
    Last edited by HallsofIvy; May 2nd 2013 at 11:15 AM.
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