Solve x! = 10 for x.

Matthias, KoH

2009-02-10 10:02 pm

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.)

回答 (1)

myisland8132

2009-02-10 11:00 pm

✔ 最佳答案

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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