Grade 10 Math

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how many integer values are there for K for which 4X squared plus KXY minus 9Y squared is factorable

  • Grade 10 Math -

    4x^2 + kxy - 9y^2

    k = (4x^2 + 9y^2)/xy

    let x = 3m and y = 2m

    k = (36m^2 + 36n^2)/6mn
    k = 6m/n + 6n/m

    So, we see that n must divide 6m and m must divide 6n

    If m=1, n divides 6: 1,2,3,6
    If m=2, n divides 12: 1,2,3,4,6,12
    and so on

    Now, how many of those values of m and m determine unique values for k, I don't know. Have fun!

  • Grade 10 Math -

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