I just immediately saw that the four sets of brackets hold a series of numbers that are incremental. And since 2x3x4x5=120 I just assumed the answer was that X=1. So within 5 seconds I thought I had the answer. I really didn't consider there may be others possible. I really need to learn to be more pedantic with these kinds of problems.
In many videos the complex solutions are not considered. I found +1 (by intuition) and -6 (since it results in -5*-4*-3*-2). Then I told myself that the complex solutions could be found easily by dividing the 4th-order polynomial by (x-1) and than by (x+6) resulting in a quadratic with complex conjugated roots. So I stopped there.
@@MathmentorX19 I'm from the UK. No, I have never taught maths but for many years I used to programme computers at from low level using machine code all the way up to object oriented code in higher languages. Seeing patterns in numbers just became second nature. 120 Stands out to me as it can be made by the product of four consecutive integers (2•3•4•5) or three consecutive integers (4•5•6) The next time this happens is the number 175560 which can be produced from either 19•20•21•22 or 55•56•57 It's yet another of those useless pieces of information that has stuck in my mind for so long, that I forget how I came to know it. Yes I know that the number 24 also fits but I don't count that as one of the integers is 1. (1•2•3•4 or 2•3•4)
The solutions x = 1 and x = -6 are obvious (120 = 2 × 3 × 4 × 5). So just multiply it all out to get the equation in standard quartic form, divide the quartic by (x -1)(x + 6) = x² +5x - 6, and all that's left is a quadratic to solve.
Helpful, informative Algebra solution
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Awesome 👏 info as usual
Thank you so much!! Thanks for watching, what country are you from?
@@MathmentorX19 USA 🇺🇸
Very astucious change of variable. Love it.
Thanks! 👍🏻
I just immediately saw that the four sets of brackets hold a series of numbers that are incremental. And since 2x3x4x5=120 I just assumed the answer was that X=1. So within 5 seconds I thought I had the answer. I really didn't consider there may be others possible. I really need to learn to be more pedantic with these kinds of problems.
In many videos the complex solutions are not considered. I found +1 (by intuition) and -6 (since it results in -5*-4*-3*-2). Then I told myself that the complex solutions could be found easily by dividing the 4th-order polynomial by (x-1) and than by (x+6) resulting in a quadratic with complex conjugated roots. So I stopped there.
Thanks for watching, what country are you from?
That's great! 👍🏻 are you a teacher of maths?
@@MathmentorX19 I'm from the UK. No, I have never taught maths but for many years I used to programme computers at from low level using machine code all the way up to object oriented code in higher languages. Seeing patterns in numbers just became second nature.
120 Stands out to me as it can be made by the product of four consecutive integers (2•3•4•5) or three consecutive integers (4•5•6) The next time this happens is the number 175560 which can be produced from either 19•20•21•22 or 55•56•57
It's yet another of those useless pieces of information that has stuck in my mind for so long, that I forget how I came to know it.
Yes I know that the number 24 also fits but I don't count that as one of the integers is 1.
(1•2•3•4 or 2•3•4)
That was good
Thank you so much!! 👍🏻
The solutions x = 1 and x = -6 are obvious (120 = 2 × 3 × 4 × 5). So just multiply it all out to get the equation in standard quartic form, divide the quartic by (x -1)(x + 6) = x² +5x - 6, and all that's left is a quadratic to solve.
Thanks for watching! 👍🏻
Sqr(121)=+11
m^2=121 ==> m^2-121=0 ==> (m+11)*(m-11)=0 ==> m=11 or m=-11
sqr(x) is only >= 0
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X=1
120=5! = 5x4x3x2x1 solved
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(x+4)! = 5! --> x+4 = 5 --> x = 1
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