A very nice olympiad maths question | x(x+2)(x+4)(x+6)=9 | You need to know this trick | Algebra

Подписаться 3,5 тыс.

Просмотров 38 тыс.

50% 1

See the way I breakdown the solution of this question. There is a lot you can learn from this video.
How to solve x(x+2)(x+4)(x+6)=9
. ENJOY
If this is your first time to my channel, here, I shared simple step by step method of solving Algebra with a simple trick.
Please like, subscribe, and share this video with your friends . Don't forget to comment if you have any questions or doubts or if you know a better way to solve this.
#education #school #learning #students #learn #exam #quiz #math #biology #academy #maths #test #exams #educational #scholarship #mathematics #_ #cbse #classes #physics #phd #registernow #campus #boardexam #speech #studentsuccess #edtech #reasoning #tutor #olimpiade #olympiadmaths #olympiadquestion #onlinemathstv
#olympiadpreparation #onlinemaths #mathchallenge #maths
#mathematics #challengingmathproblems #onlinemathtutor
#challengingquestions #olympiad2022
#olympiadmathematicscompetition #olympiadmathematicalquestion
#polynomials #polynomialequations
#polynomialsandfactorisation9thclassapandts #polynomialsclass9

Опубликовано:

23 апр 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 32

@molibdenum 2 месяца назад

My approach is by defining an intermediate variable based on the halfway point between the factors. For example, in (x+0)(x+2)(x+4)(x+6), 3 is halfway between 0 and 6, so I set y = x + 3. This gives a new equation (y-3)(y-1)(y+1)(y+3) = (y^2-1)(y^2-9) = (z+4)(z-4) = 9 where we set z = y^2 - 5. From this we solve backwards. z^2 - 16 = 9, so z = +/- 5. y^2 = z + 5, so y^2 = 10 or 0. x = y - 3, so x = -3, -sqrt(10)-3, +sqrt(10) -3.

@SpencersAcademy 2 месяца назад

Awesome, I like that. This is fantastic.

@davidbrisbane7206 2 месяца назад

Very clever 👏👏👏

@mawavoy 29 дней назад

An excellent problem

@carlorff1965 Месяц назад

03:31 I made it short and easy by using reduced quadratic equation formula a^2+px+q a_1=-(p/2)+sqrt((p/2)^2-q) a_2=-(p/2)-sqrt((p/2)^2-q) plug the values in: a_1=-4+sqrt(4^2+9)=1 a_2= -4-sqrt(4^2+9)=-9 07:47 and following: did the same there. Works fine. 👍😃 👍

@SpencersAcademy Месяц назад

That's fantastic.

@harrymatabal8448 2 месяца назад

Cool my man

@amgalanbaatar6769 2 месяца назад

Now i understand 😅

@herbertklumpp2969 2 месяца назад

You get a^2+8a'-9=0. Therefore (a -1)*(a+9) =0 then you have to Solve 2 easy quadratic equations a^2 +6x +9=0 conclude ( a +3)^2=0 a=-3 or x^2 +6x -1=0 easy with quadratic Formular. X= -3 + - sqrt( 10) thsts all

@KingGisInDaHouse 2 месяца назад

Bruh you had two cases where completing the square was easier then factorizing or the quadratic formula

@mightyhero Месяц назад

There are 4 terms that multiply to get 9. The only way to get 9 is if the terms are something like 3 x 3 x 1 x 1. To get (x + 6) to be one of the 3s, x = -3. The rest of the terms fit x(x+2)(x+4)(x+6) = -3(-1)(1)(3) = 9.

@timbond6176 Месяц назад

все можно проще: z=x+3 (z-3)*(z-1)*(z+1)*(z+3)=9 (z^2-9)*(z^2-1)=9 z^2=t (t--9)(t-1)=9 t^2-10t +9=9 t^2-10t=0

@adakwok1848 Месяц назад

Idk why when I looked at the question I immediately thought of -3, tried it, and it worked lol

@tommyliu7020 Месяц назад

This is a quartic equation. Shouldn’t there be 4 solutions for x?

@anindyakar5336 2 месяца назад

-3

@mathstricknguon2246 Месяц назад

X^2+6X=t

@mohinkhan2503 2 месяца назад

@GiperManYT Месяц назад

(х^2+6х+8)(х^2+6х)=9

@timber72 2 месяца назад

x = -3

@bernardburdick9264 Месяц назад

Too me 10 sec.

@kccheung1059 Месяц назад

一3 in 20 seconds

@harukanapapa Месяц назад

t=x-3 (t-3)(t-1)(t+1)(t+3)=9 (t^2-9)(t^2-1)=9 t^4-10t^2+9=9 t^4-10t^2=0 t^2(t^2-10)=0 ∴t=0,t=±√10 ∴x=-3,-3±√10

@SpencersAcademy Месяц назад

Fantastic. You nailed it

@user-eo8fw2ij4i Месяц назад

Let x+3 = y (y-3)(y-1)(y+1)(y+3)=9 (y^2-9)(y^2-1)-9=0 y^4-9y*2-y*2+9-9=0 y*4-10y*2=0 y*2(y*2-10)=0 y = 0 y= sqrt(10) y= -sqrt(10) x= -3 x= -3+sqrt(10) x= -3-sqrt(10)

@SpencersAcademy Месяц назад

Excellent. You nailed it, man.

@ChavoMysterio Месяц назад

x(x+2)(x+4)(x+6)=9 (x²+6x)(x²+6x+8)=9 Let y=x²+6x y(y+8)=9 y²+8y=9 y²+8y-9=0 (y+9)(y-1)=0 y-1=0 x²+6x-1=0 x²+6x+9=10 (x+3)²=10 |x+3|=√10 x+3=±√10 x=-3±√10 ❤❤ y+9=0 x²+6x+9=0 (x+3)²=0 x+3=0 x=-3; multiplicity of 2 ❤️ ❤

@SpencersAcademy Месяц назад

Fantabulous. You are really on point, man.