場在 發問於 科學及數學數學 · 5 年前

Some different kinds of questions?

Factorize 2a^(n+1)-7a^n-30a^(n-1)

find the range of values of k that equation x^2+(k -2)x+1=0 has real roots

Simultaneous equation y=x^2-7x+2,y=x-(5k+4) have only one set of real solution and k is constant.find k

更新:

1.Factorize 2a^(n+1)-7a^n-30a^(n-1)

find the range of values of k that equation x^2+(k -2)x+1=0 has real roots

Simultaneous equation y=x^2-7x+2,y=x-(5k+4) have only one set of real solution and k is constant.find k

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    Factorize 2a^(n+1)-7a^n-30a^(n-1)

    2aⁿ⁺¹ - 7aⁿ - 30aⁿ⁻¹

    = (2a²) aⁿ⁻¹ - (7a) aⁿ⁻¹ - 30 aⁿ⁻¹

    = aⁿ⁻¹ (2a² - 7a - 30)

    x² + (k - 2) x + 1 = 0

    ∵ The equation has real roots

    ∴ Δ ≥ 0

    (k - 2)² - 4 (1) (1) ≥ 0

    k² - 4k + 4 - 4 ≥ 0

    k (k - 4) ≥ 0

    k ≤ 0 or k ≥ 0

    y = x² - 7x + 2       y = x - (5k + 4)

    x² - 7x + 2 = x - (5k + 4)

    x² - 7x + 2 - x + (5k + 4) = 0

    x² - 8x + (5k + 6) = 0

    ∵ The equations have one set of real solution

    ∴ Δ = 0

    (-8)² - 4 (1) (5k + 6) = 0

    64 - 20k - 24 = 0

    20k = 40

    k = 2

    7.

    Since ABCD is a rectangle,

    BE = DE

    x + 6 = 3x - 2

    3x - x = 6 + 2

    2x = 8

    x = 4

    ∴ D. 4

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