? 發問於 科學及數學數學 · 2 月前

Maths problem how to do, thanks?

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I don't know how to do questions 4, thanks

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  • 2 月前
    最愛解答

    兩題都不能完全算出結果, 只能用 k 的函數表示.

    Let k be a constant. If the roots of the

    quadratic equation x^2-5x+k = 0 are α and β,

    find α^3β+5αβ^2.

    [Sol.]

    α^3β+5αβ^2

        = αβ(α^2-5α+k)+5α^2β-kαβ+5αβ^2

        = 5αβ(α+β)-kαβ

        = 5k(5) - k(k)

        = 25k-k^2 = k(25-k)

    If α≠β and {6α-α^2 = k, 6β-β^2 = k},

    find (α-β)^2.

    [Sol.]

    α, β are solutions of equation

        x^2 - 6x + k = 0

    So,

        α + β = 6, αβ = k

     (α-β)^2 = (α+β)^2-4αβ

          = 6^2 - 4k

          = 36 - 4k

    α ≠ β if and only if k ≠ 9.

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