Solve x! = 10 for x.

Solve x! = 10 for x.

Definition :

For integer x > 1, x! = x(x-1)(x-2)...1

For non-integer x > 1, x! = x(x-1)(x-2)...(x-[x]+1)

where [x] is the integral part of x.

e.g. : 4.12! = 4.12 x 3.12 x 2.12 x 1.12 = 30.52148736

(Please show clear steps.

The best result is to find the exact value of x.

Numerical methods are also welcomed and please give your

answer up to 8 d.p. Try not to use bisection method.)

1 個解答

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  • 1 十年前
    最愛解答

    Solve x! = 10 for x

    By common sense, the answer should be between 3 and 4

    So x! should be equal to

    x(x-1)(x-2)=10

    That is x^3-3x^2+2x-10=0

    Actually, you can use the formula to get the exact result if you are interested. Instead, I would like to give the numerical answer by using Newton's method.

    X[1] = 3.46172480826952

    X[2] = 3.31879972927447

    X[3] = 3.30895677385238

    X[4] = 3.30890734373402

    X[5] = 3.30890731977616

    X[6] = 3.3089073197651

    X[7] = 3.30890731976509

    X[8] = 3.30890731976509

    X[9] = 3.30890731976509

    So x=3.30890731976509

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