Oui j'ai résolu comme vous

I did it pretty much the same way. Took me 20 seconds in my head, maybe less. Since it is a factorial, we know that x+ 2 is a positive integer, and we know that 1680 must be the product of four consecutive integers. It's obvious that combinations like 2-3-4-5 and 3-4-5-6 are too low, so we quickly multiply 4-5-6-7 (still too low) 5-6-7-8 (just right) . Since we know that x+6 (the highest number in the sequence) is 8, x must be 2. I like your additional bit of logic, stipulating that 5 and 7 must be two of the factors., therefore the only possibilities are 4-5-6-7 and 5-6-7-8. I didn't think of that. I think that would have slowed me down, because I can multiply faster than I factor, but well played!

I did it the same way in 1mn. It’s arithmetical not algebrical. It’s mandatory to use positive integers only. Factorization is the right approach.

It works cos the answers are whole, otherwise his method works.

@@adelsamani7917 I disagree. As long as you are considering factorials, the result is obviously an integer. That’s arithmetic not algebraic.

Thank you very much!

Why indian ? Why man ? Why intelligent ?😉🤭

That's how I did it! Soooo much easier 😊

@@tonitalas1757 And then you missed the second answer -11!

@@yung-kanglee4681 except that factorials are only defined for non negative integers or if you get rather fancy in your math you can extend it to non negative numbers as a whole but that gets kinda funky and beyond the scope here i think. either way you's ended up with (-5)!/(-9)! plugging that in which is not defined in either the numerator or denominator and as such is not actually a solution to the problem

@@johnpaullogan1365 yes, you are so smart!!!

Good

Thank you very much

Ta méthode est parfaitement mathématique. L'autre méthode étant d'une lourdeur peu mathématiques

Thank you very much

Thank you very much!

Да, но это ответ для другого уравнения. Плюс решение подбором не засчитывается на олимпиадах (да и на обычных уроках...)

x=2,0151951952 ?

Thanks 👍👍👍 X>-2

but 0!=1. so it is defined at x=-2 in other words, there was no mistake made. x CAN BE >=-2. only because the factorial is involved.

@@user-vx4lb8rj8r and you're righter than me... sorry @learncommunolizer!