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? asked in Science & MathematicsMathematics · 4 years ago

If x = y and x^2y^2 - 5xy + 6 = 0, then which of the following is possible? The answer is x^2 = 3 but how?

4 Answers

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  • roderick_young
    Lv 7
    4 years ago
    Favorite Answer

    Let u = x^2. Then u=y^2, too. And for that matter, u=xy . The second equation becomes

    u^2 - 5u + 6 = 0, which is a quadratic, and factors into

    (u - 3) (u - 2) = 0

    can you take it from there?

  • Como
    Lv 7
    4 years ago

    x^4 - 5 x^2 + 6 = 0

    [ x^2 - 3 ] [ x^2 - 2 ] = 0

    x^2 = 3 , x^2 = 2

  • ?
    Lv 7
    4 years ago

    x = y

    x^2y^2 - 5xy + 6 = 0

    x^4 - 5x^2 = -6

    x^2(x^2 - 5) = -6

    x^2 = 3

  • ?
    Lv 7
    4 years ago

    x^2y^2 - 5xy + 6 = 0

    (xy - 2)(xy - 3) = 0

    That means xy = 2 or 3. Since x = y, just substitute x for y; x times x is x^2, so x^2 = 2 or 3. Same thing with y^2.

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