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March 25, 2017

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If p≠q and p² = 5p-3 and q² = 5q-3 the equation having roots as p/q and q/p is

  • algebra - ,

    well
    p = (5±√13)/2
    q = (5±√13)/2

    If p≠q then one is (5+√13)/2 and the other is (5-√13)/2

    (5+√13)/(5-√13) = (19+5√13)/6
    (5-√13)/(5+√13) = (19-5√13)/6

    So, the equation is

    (x-((19+5√13)/6))(x-((19-5√13)/6)) = 0
    (6x-19-5√13)(6x-19+5√13) = 0
    (6x-19)^2 - 325 = 0
    36x^2 - 228x + 36 = 0
    3x^2 - 19x + 3 = 0

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