Thanks, professor! Always explaining step by step, that's the very best way to teach! Keep it!
@PreMath
2 жыл бұрын
You are very welcome. Glad to hear that! Thank you for your feedback! Cheers! You are awesome 😀 Love and prayers from the USA!
@pwmiles56
2 жыл бұрын
Nice but ... you can use the symmetries of the equation. Multiply out denominator and rearrange (x+2)(x+3)(x+4)(x+5) - (x-2)(x-3)(x-4)(x-5) = 0 The x^4 terms cancel. So do the constant terms. Also, the x^2 terms cancel (because the x^2 terms in the right hand product are the same as in the left hand product). We are left with Ax^3 + Bx = 0 x=0 is a solution. For the others you can inspect to get A/2 = 2 + 3 + 4 + 5 = 14 B/2 = 2.3.4 + 3.4.5 + 4.5.2 + 5.2.3 = 24 + 60 + 40 + 30 = 154 x = +/- i sqrt(154/14) = +/- i sqrt(11)
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome 😀
@TheFlax33
2 жыл бұрын
My first attack at this equation was yours and after I multiply out denominator I immediately quick check if x=0 is a possibility, which is often. Thanks for the breakdown.
@blucy10
2 жыл бұрын
That is how I solved it
@mohamedbrahim8757
2 жыл бұрын
Did it the same way. it is less intelligent but much more simpler!
@claudiogrossi2438
2 жыл бұрын
Sono veramente contento di avere scoperto questo canale. A 60 anni mi sto riappassionando alla matematica come quando la studiavo alle scuole superiori, ormai troppi anni fa.
@PreMath
2 жыл бұрын
Bello sentirlo. Eccellente! Grazie per aver condiviso! Saluti! Sei fantastico Claudio 😀 Amore e preghiere dagli USA!
@siddhantofpremath1788
2 жыл бұрын
Thanks Sir, You teaching must be appreciated Because you teach step by step by explaining each line and each equation perfectly... Keep it up.. Sir!
@PreMath
2 жыл бұрын
You are very welcome. Thank you for your feedback! Cheers! You are awesome 😀 Love and prayers from the USA!
@RandomGuy-yf4wf
2 жыл бұрын
Creative name and picture 👌.
@siddhantofpremath1788
2 жыл бұрын
@@RandomGuy-yf4wf thank you ..!
@benjaminkarazi968
2 жыл бұрын
Hello, I congratulate you for your manners and patients; a hard-to-find personality. Regards,
@TheFlax33
2 жыл бұрын
Thanks for all you have been doing. I'm a big fan. Blessings to you and yours. ✌
@PreMath
2 жыл бұрын
You are very welcome. So nice of you. Thank you for your feedback! Cheers! You are awesome dear 😀 Love and prayers from the USA!
@HappyFamilyOnline
2 жыл бұрын
Great explanation👍 Thank you so much for sharing😊😊
@PreMath
2 жыл бұрын
You are very welcome. Thank you for your feedback! Cheers! You are awesome 😀
@prohind
2 жыл бұрын
One can form thousands of such questions by replacing 2,3,4,5 with any other similar set such as 3,4,5,6 or 4,5,6,7 etc. All these expresions would be equal to one when x=0. The trick here lies in keeping the number of sub expressions within small brackets as even so that denominator resultant number is positive when x=0. Also if nominator and denomintor are interchanged, the value of expression would remain 1 when x=0. Some examples: ((x-2)(x-3)) / ((x+2)(x+3)) =1 ((x+9)(x+10)(x+20)(x+6)) / ((x-9)(x-10)(x-20)(x-6)) =1 ((x+2)(x+3)(x+4)(x+5)(x+6)(x+7)) / ((x-2)(x-3)(x-4)(x-5)(x-6)(x-7)) =1 ......
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome 😀
@RashmisABCD
2 жыл бұрын
Your video looks neat and well organised as well, great content you shared with us, , have a wonderful day, Stay healthy and safe , lk266
@PreMath
2 жыл бұрын
So nice of you. Thank you for your feedback! Cheers! You are awesome Rashmi 😀 Love and prayers from the USA!
@JD_ALMIGHTY
2 жыл бұрын
Was a very interesting sum. Respect sir
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome Jaydev 😀 Love and prayers from the USA!
@shubhmishra66
2 жыл бұрын
It's a problem, not a sum ... Sum is for addition only!
@KAvi_YA666
2 жыл бұрын
Thanks for video. Good luck!!!!!!!!! Mathematics of my favourite subject.
@PreMath
2 жыл бұрын
You are very welcome. Thank you for your feedback! Cheers! You are awesome 😀 Love and prayers from the USA!
@dharitrimoharana4719
2 жыл бұрын
Nice question and explanation. Btw it can also be easily solved through Vieta's realation.
@user-my7ki4it3s
2 жыл бұрын
Nice one. But I decided to rewrite (x^2 + 7x + 10)(x^2 + 7x + 12) and (x^2 - 7x + 10)(x^2 - 7x + 12) as (x^2 + 7x + 11)^2 - 1 and (x^2 - 7x + 11)^2 -1 correspondly. Then we obtain eq (x^2 + 7x + 11)^2 - 1 = (x^2 - 7x + 11)^2 - 1. Ones on both sides are gone, everything to left-hand side: (x^2 + 7x + 11)^2 - (x^2 - 7x + 11)^2 = 0. Using the difference of squares formula gives us an eq: 14x*(2x^2 + 22) = 0. Divide by 28 to simplify: x*(x^2 + 11) = 0. Therefore we get the answer: x = 0, x = sqrt(11)*i, x = -sqrt(11)*i
@opytmx
2 жыл бұрын
Very interesting solution with the imaginary numbers. I thought it was a fun problem, as x = 0 can be spotted immediately. The nominator and denominator have an even number of factors, hence 2 * 3 * 4 * 5 = (-2) * (-3) * (-4) * (-5) = 120, and 120/120 = 1 ;-)
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome 😀
@jisamahmed9075
2 жыл бұрын
Wonderful solution! Love from Bangladesh sir 😊
@PreMath
2 жыл бұрын
Excellent! Glad to hear that! Thank you for your feedback! Cheers! You are awesome Jisam 😀 Love and prayers from the USA!
@srividhyamoorthy761
2 жыл бұрын
A very Interesting Sum, thanks Once again Sir
@PreMath
2 жыл бұрын
You are very welcome. Thank you for your feedback! Cheers! You are awesome Moorthy 😀
@242math
2 жыл бұрын
Very well explained bro. Thanks for sharing this rational equation.
@PreMath
2 жыл бұрын
Glad it was helpful! Thank you for your feedback! Cheers! You are awesome my friend 😀 Love and prayers from the USA!
@Nil_11186
2 жыл бұрын
Actually this is quite a type of quadratic equation so u can do the first steps in a way of multiplication is distributive over addition and subtraction and then factorisation using identities
@theroastingboy7548
2 жыл бұрын
Very interesting and enjoying question salute sir
@PreMath
2 жыл бұрын
Excellent! Glad to hear that! Thank you for your feedback! Cheers! You are awesome 😀 Love and prayers from the USA!
@pranavamali05
2 жыл бұрын
What a question thnx a lot
@PreMath
2 жыл бұрын
You are very welcome. Thank you for your feedback! Cheers! You are awesome Pranav 😀 Love and prayers from the USA!
@philipkudrna5643
2 жыл бұрын
Before watching: I did the „long way“ by multiplying everything and the only non-complex/imaginary solution I could find is x=0 (which yields 120/120=1). Maybe there is a more efficient way? Now I watch the video. Hm, not so sure, whether the substitution approach is really faster…!
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome Philip 😀
@bobtivnan
2 жыл бұрын
After thinking about it for a while, I could see that zero would be a solution by guessing. I thought I was done not realizing the other solution could be complex. I also wondered if combinations could help here since this looks like (x+5 choose 4) / (x-2 choose 4).
@kwa6022
2 жыл бұрын
It is easily seen that the coefficient of x^4 and x^0 are equal. Hence, by cross-multification and rearrangement, it was reduced to a cubic equation with x as a factor. Then the problem remained is a quadratic equation. //
@HassanLakiss
2 жыл бұрын
Thank you for a very interesting question which you solved nicely.
@S.F663
2 жыл бұрын
Thank you🌹🌹🙏
@PreMath
2 жыл бұрын
You are very welcome. Thank you for your feedback! Cheers! You are awesome Engineer 😀 Love and prayers from the USA!
@rangaswamyks8287
2 жыл бұрын
Namasthe sir If we put x=0 The value of expression Becomes E=1 My question is If we multiply the factors In denominater and numirator Can we get 1..may not be possible.. Please clarify sir
@PreMath
2 жыл бұрын
Yes, we'll still get the same answer. However, that approach would be very tedious. Therefore, I manipulated the problem to keep things simple! Thanks for asking. You are awesome Rangaswamy 😀
@rachidbenmeziane4968
2 жыл бұрын
simple, clear and nice, really I like it !
@shaswatpramanik6814
2 жыл бұрын
This is good question, really good question, But is there any other method of solving?
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! There are many approaches to solve this. However, try to make things simple. You are awesome Shaswat 😀
@jarikosonen4079
2 жыл бұрын
Is the x=0 "double root" here? In the expanded form x^4 can be cancelled, so only 3 roots remain.
@l.w.paradis2108
Жыл бұрын
Yes.
@johnbrennan3372
2 жыл бұрын
Very good method,nicely thought out.
@PreMath
2 жыл бұрын
Thanks a lot John You are awesome 😀
@cellics
2 жыл бұрын
I could get zero just by fiddling with integer. Didn't think there were other roots. Thanks for an interesting video!
@PreMath
2 жыл бұрын
Happy to help! You are very welcome. Thank you for your feedback! Cheers! You are awesome 😀
@ramanivenkata3161
2 жыл бұрын
Though a simple sum, Excellent deduction of ' X' value. Step by step teaching needs more patience. 👍
@PreMath
2 жыл бұрын
Glad it was helpful! Thank you for your feedback! Cheers! You are awesome Ramani 😀
@d.m.7096
2 жыл бұрын
Both numerator and denominator are degree-4 polynomials. Hence there should be at most 4 distinct roots. But your solution gives only 3 roots. Where is the 4th root?
@davidtesar8195
2 жыл бұрын
The denominator implies that X cannot be 2, 3, 4, or 5. We also know that the numerator and denominator must be equal. The product of four larger numbers can never equal the product of four smaller numbers. So we need to add symmetry. We can see from the individual terms that zero is the number that will give us that symmetry. An even number of terms will give us a positive number in the denominator. In other words, the whole problem simplifies to the question: for which number does is abs(x + 2) = abs(x - 2)? Zero is the only possible answer.
@rockyjohnson6248
2 жыл бұрын
This holds true only for real values of x.
@wackojacko3962
2 жыл бұрын
Both solutions viable...it's like a tangible object and the reflection of that object in a mirror.
@PreMath
2 жыл бұрын
Great observation! Thank you for your feedback! Cheers! You are awesome 😀 Love and prayers from the USA!
@vaghelabhikhusing6553
2 жыл бұрын
Good work sir 💕💕💕💕💕💕💕
@PreMath
2 жыл бұрын
Excellent! Glad to hear that! Thank you for your feedback! Cheers! You are awesome Vaghela😀 Love and prayers from the USA!
@s1ng23m4n
2 жыл бұрын
x = 0 is obvious root. if we will use cross multiplying and expand brackets we will get something very nice ;)
@s1ng23m4n
2 жыл бұрын
x^4 and the last constant will be cancelled from both sides and in the rest we will get 28x^2 + 308 = 0 which has no solution.
@PreMath
2 жыл бұрын
Excellent! Thank you for sharing! Cheers! You are awesome 😀
@ravikrpranavam
2 жыл бұрын
If we put x=0in the above equation we get 120/120 , hence =1
@jim2376
Жыл бұрын
By inspection x = 0. 120/120 = 1
@haydenwong659
2 жыл бұрын
I know pretty much nothing about special rules or what but I'd just expand the equation and the bottom and top are the same.
@usman_mmalik
2 жыл бұрын
Superb!
@nicholascage3699
2 жыл бұрын
Math is fun ,go for easy question to build your confidence
@PreMath
2 жыл бұрын
You are awesome 😀
@ايمنكويكي
2 жыл бұрын
Thanks !
@PreMath
2 жыл бұрын
You are very welcome. You are awesome 😀 Love and prayers from the USA!
@SuperYoonHo
2 жыл бұрын
awesome!
@TheOlesb
2 жыл бұрын
As there are only 4 brackets on each line and minus X minus=+ it's easy to see x=0
@navjotkalsi2807
2 жыл бұрын
Keep it up. Awesome question.
@PreMath
2 жыл бұрын
Excellent! Glad to hear that! Thank you for your feedback! Cheers! You are awesome Navjot dear 😀 Love and prayers from the USA!
@navjotkalsi2807
2 жыл бұрын
@@PreMathsir, you are from which state?
@PreMath
2 жыл бұрын
@@navjotkalsi2807 Arizona
@navjotkalsi2807
2 жыл бұрын
@@PreMath which city sir?
@navjotkalsi2807
2 жыл бұрын
I'm a maths teacher. I have done masters in mathematics and bachelor in education. (M.sc. maths B.ed.) I am having six years of teaching experience. I want to come to USA. My brother is in Michigan state. Can you please guide me what should I do? Can you please help me 🙏
@furzaanullah8114
2 жыл бұрын
Very nice 👍👍👍. Sorry, for I was late.
@PreMath
2 жыл бұрын
Thanks for coming. You are the best Furzaan. 😀 Love and prayers from the USA!
@nicogehren6566
2 жыл бұрын
nice question
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome Nico 😀 Love and prayers from the USA!
@susantagarai7647
2 жыл бұрын
Can you explain 7x=-7x ie 7=-7 ?
@whatzause
2 жыл бұрын
I greatly enjoy these videotorials but I often think: If this is “PREmath“ how involved must “math“ be!
@justmath331
2 жыл бұрын
Did it using componendo dividendo
@susennath6035
2 жыл бұрын
Nice
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome Susen 😀 Love and prayers from the USA!
@rajsekhar8227
2 жыл бұрын
Love from india 🥰
@PreMath
2 жыл бұрын
Thank you Raj You are awesome 😀 Love and prayers from the USA!
@giuseppemalaguti435
2 жыл бұрын
28x^3+308x=0.....x=0....(forse,ho fatto i calcoli a mente)
@wesleysuen4140
2 жыл бұрын
But iota doesn’t have any tittle (the dot over the letter i)!!
@mda99das
2 жыл бұрын
you can solve this in under 10 seconds if you just think what it represents, and just see what happens when x =0
@playgirl7305
2 жыл бұрын
My God, I just saw the equation and put and replaced x to be =0. Eureka! The equation was solved within 15 seconds.
@billcame6991
2 жыл бұрын
Looking at it, it seems like x=0 would do it.
@gangeet2007
2 жыл бұрын
if we substitute x=0 it is not true
@kfjfkeofitorhf9520
Жыл бұрын
24(5)/24(5) 120/120=====1 X=0
@nirupamasingh2948
2 жыл бұрын
Vnice
@PreMath
2 жыл бұрын
Glad to hear that! Thank you for your feedback! Cheers! You are awesome Niru 😀 Love and prayers from the USA!
@nirupamasingh2948
2 жыл бұрын
@@PreMath 🙏🙏getting to learn beautiful techniques
@Teamstudy4595
2 жыл бұрын
4th comment and my ans is 0
@PreMath
2 жыл бұрын
Super job
@dansf2
2 жыл бұрын
The yungin's today don't say "imaginary" numbers. It's complex. But nice one.
@seamanreal3862
2 жыл бұрын
Show!!!
@karadeniz8609
2 жыл бұрын
I am find 10 second x=0
@PreMath
2 жыл бұрын
Excellent! Glad to hear that! Thank you for your feedback! Cheers! You are awesome Kara 😀
@ABHIGAMING-yo9my
2 жыл бұрын
0
@PreMath
2 жыл бұрын
Excellent! You are awesome Abhi 😀
@chaparral82
2 жыл бұрын
x=0, just looking
@PreMath
2 жыл бұрын
Excellent! You are awesome 😀
@緑孔雀
2 жыл бұрын
X=0
@PreMath
2 жыл бұрын
Excellent! Thank you for your feedback! Cheers! You are awesome 😀 Love and prayers from the USA!
@timspooner59
2 жыл бұрын
One value zero and the other imaginary. Hard to see a use for this
@devondevon4366
2 жыл бұрын
X equals 0
@Jimmy-tv8tv
2 жыл бұрын
One minute get result.
@maximusminimus8050
2 жыл бұрын
x=0? Ouch
@raomaruthy484
2 жыл бұрын
X Value zero
@marshalls36
2 жыл бұрын
好
@onesguen2210
2 жыл бұрын
0
@PreMath
2 жыл бұрын
Excellent! You are awesome 😀
@onesguen2210
2 жыл бұрын
@@PreMath math teacher
@mustafizrahman2822
2 жыл бұрын
x=0
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome Mustafiz 😀 Love and prayers from the USA!
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