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Factor 720 to 2^4 x 3^2 x 5, then find 3 consecutive integers you can form by mulitplying the factors, you get 8 x 9 x 10 = 720. X+1 is therefore 7, so X = 6.
I did the same method, but I think, if the number (720) was taller, our method will be too much hard. The method in the video is so much stylisher than ours ^^
that helps one to find the answer,but does not meet the requirement of the math logic. it's actually a cubic equation that you need to find for this particular math problem.write down that equation certainly matters in an olympiad exam.
(x+4)! / (x+1)! = 720 (x+4)(x+3)(x+2) = 10*9*8 x+4=10, x+3=9, x+2=8 x=6 1. x+1, x+2, x+3, x+4 and then x too - are natural 2. 720 = 10*9*8 - the is no other solutions for three natural numbers n+2, n+1, n
No, tere is no complex "solutions" because factorial is defined for non-negative interger numbers - x+1, x+2, x+3, x+4 etc. are NATURAL numbers Otherwise - what is factorial of 8.5+i*sqr(239)/2 ?
NO. There is no consent. 1. The problem uses the factorial symbol, not the gamma function symbol. And the factorial is only defined for natural numbers and 0. 2. "determined" - this is the keyword. The gamma function is only related to the factorial for natural numbers. 𝚪(n) = (n - 1)! - that is, gamma for a natural number is not equal to the factorial of this number. The gamma function is not a generalization of the factorial to complex numbers. 3. To be sure, I checked the gamma function values for those given in the user-nr9cs8fd5q entry complex solutions of a quadratic equation. They are in no way solutions to the original problem, because for the negative real part the gamma function takes complex values very close to 0 for both the real and imaginary parts. Therefore, you will not be able to get the value 720 by multiplying 3 such numbers. 4. If, as you claim, other solutions are possible, prove it.
