F4 Math ~~ Help

Let f(x) = 3x3 – 9x2 – 14x + 8 .

A, B and C can complete the same piece of work alone in x hours, ( x – 1 ) hours and ( x + 2 ) hours respectively. If they work together, they can complete the work in 1 hour and 20 minutes.

(i) Show that 3 (x^3) – 9 (x^2) – 14x + 8 = 0. (+ explanation)

(ii) Find the value(s) of x.

Thanks~~~~~

1 個解答

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  • 8 年 前
    最佳解答

    a)

    A can complete a job in x hours

    so A complete 1/x work in an hour

    B can complete a job in x hours

    so B complete 1/(x-1) work in an hour

    C can complete a job in x hours

    so C complete 1/(x+2) work in an hour

    ·.·They take 1 hour and 20 mins to complete the work together .

    1/x + 1/(x-1) + 1/(x+2) work will be completed in 1/(80/60)=1/(3/4) hour.

    1/x + 1/(x-1) + 1/(x+2) = 1/(4/3)

    (x-1)(x+2)+x(x+2)+x(x-1) / x(x-1)(x+2) = 3/4

    x²+2x-x-2+x²+2x+x²-x / x³-x²-2x = 3/4

    3x³-3x²-6x = 12x²+8x-8

    3x³-9x²-14x+8 = 0

    b)

    3x³-9x²-14x+8 = 0

    (x-4)(3x²+3x-2) = 0

    x=4 or 1/6(-3-√33) or 1/6(√33-3)

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