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Math Help - To see a solution to a 2nd degree equation without using the regular formula

  1. #1
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    Question To see a solution to a 2nd degree equation without using the regular formula

    This might be a little to advanced for this forum, but I think it is a little bit to easy to post in linear algebra. My question is if there is a quick way to see the solution of this equation, solving y as a function of x, without using the 2nd degree equation formula. Here it is:
    y^{2}(1+4a)-8axy+x^{2}(-1+4a)=0
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  2. #2
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    Re: To see a solution to a 2nd degree equation without using the regular formula

    Quote Originally Posted by fysikbengt View Post
    This might be a little to advanced for this forum, but I think it is a little bit to easy to post in linear algebra. My question is if there is a quick way to see the solution of this equation, solving y as a function of x, without using the 2nd degree equation formula. Here it is:
    y^{2}(1+4a)-8axy+x^{2}(-1+4a)=0
    1. By first inspection you see that y = x.

    2. Divide the LHS of the equation by (y - x). (Use long division)
    You should come out with

    x(1 - 4a) + y(4a + 1)

    3. Now solve for y:

    x(1 - 4a) + y(4a + 1) = 0
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  3. #3
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    Re: To see a solution to a 2nd degree equation without using the regular formula

    Quote Originally Posted by earboth View Post
    1. By first inspection you see that y = x.

    2. Divide the LHS of the equation by (y - x). (Use long division)
    You should come out with

    x(1 - 4a) + y(4a + 1)

    3. Now solve for y:

    x(1 - 4a) + y(4a + 1) = 0
    Thanks, I dont think I would have come up with that myself, but now it is clear. From the physical interpretation it is obvious that y = x is a (superfluos) solution, and although it is not trivial to perform the long division it is easier if you know what you are looking for.
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