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Math Help - straight line and function

  1. #16
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    Re: straight line and function

    thank you ebaines,

    now the answer is complete , please look at this
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  2. #17
    MHF Contributor ebaines's Avatar
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    Re: straight line and function

    That's fine as far is goes, but of course is not a complete proof. I assume you have worked out a proof of the statement that the difference of two squared odd numbers must be divisible by 8, right?
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  3. #18
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    Re: straight line and function

    Quote Originally Posted by ebaines View Post
    That's fine as far is goes, but of course is not a complete proof. I assume you have worked out a proof of the statement that the difference of two squared odd numbers must be divisible by 8, right?
    that is
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  4. #19
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    Re: straight line and function

    I like it is a very interesting discussion. I think we can approach the question as under:
    let a = 2m+1, b = 2n +1 and c= 2p +1
    now discriminant of bx^2 + ax + c = 0 is D = a^2 - 4 bc = ( 2m+1)^2 - 4 ( 2n +1) ( 2p+1) = 4m^2 + 4m + 1- 4 [ 4 np + 2 (n+p) +1 ]
    = 4m^2 + 4m - 4 [ 4 np + 2 (n+p) ] - 3 = 4 [ m^2 + m - 4 np - 2 (n+p) ] - 3
    Now we observe that it is not a perfect square. Thus the roots will be irrational.
    Thanks from abualabed
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  5. #20
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    Re: straight line and function

    hi. ibdutt

    how did you know that 4 [ m^2 + m - 4 np - 2 (n+p) ] - 3 is not a perfect square?
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  6. #21
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    Re: straight line and function

    It has three variables m , n and p.
    the expression for ( a+b+c)^2 = a^2+b^2+c^2 + 2ab + 2bc + 2 ca
    that is why
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