Another (not necessarily better) method: The left side reduces to the product of four consecutive even numbers or four consecutive odd numbers: (x - 2)(x - 4)(x - 6)(x - 8). The prime decomposition of the right side is (2^7)(3^2)(5). One can not create four odd numbers (only three are available in the prime composition), so the left side must be the product of four consecutive even numbers. Dividing each of the four consecutive even numbers by 2 means that now we need to create four consecutive numbers using the following: 2, 2, 2, 3, 3, 5. With such a small set of numbers, we can check. 1, 2, 3, 4 is missing a "3" and a "5." 2, 3, 4, 5 is missing a "3." 3, 4, 5, 6 works. Multiplying each by 2 gives 6, 8, 10, 12. x - 2 = 12 gives us x = 14. The bigger question for me is why have I never heard of double factorial. Did I accidentally doze off for a few minutes in a Discrete Math class?
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Another (not necessarily better) method:
The left side reduces to the product of four consecutive even numbers or four consecutive odd numbers: (x - 2)(x - 4)(x - 6)(x - 8).
The prime decomposition of the right side is (2^7)(3^2)(5).
One can not create four odd numbers (only three are available in the prime composition), so the left side must be the product of four consecutive even numbers.
Dividing each of the four consecutive even numbers by 2 means that now we need to create four consecutive numbers using the following: 2, 2, 2, 3, 3, 5.
With such a small set of numbers, we can check.
1, 2, 3, 4 is missing a "3" and a "5."
2, 3, 4, 5 is missing a "3."
3, 4, 5, 6 works.
Multiplying each by 2 gives 6, 8, 10, 12.
x - 2 = 12 gives us x = 14.
The bigger question for me is why have I never heard of double factorial. Did I accidentally doze off for a few minutes in a Discrete Math class?
I’m glad you found the video helpful! 💯🙏🤩💕Thanks for sharing your method! 🔥🔥✅💕