I used an other method. y=x-6. You substitute and add the first fraction with the last and add the two others. You keep the -4. In the end, you have (y^2-4)/(y^2+5y+4) + (y^2-6)/(y^2+5y+6) =-2. (We simplify by 2). Let a=y^2+5y+5 b=y^2-5 We substitute, we developp and we have. (ab+1)/(a^2-1)=-1 (We simplify by 2 again) a^2+ab=0 a(a+b)=0 a=0 ou a+b=0 And after it is easy.
Each term in LHS add 1 --> RHS=0 Simplifying yields common numerator 2(x-6) which can be cancell out giving: [1/(x-2)]+[1/(x-3)]+[1/(x-4)]+[1/(x-5)=0 Add the two terms in the middle as well as the remaning two, yielding common numerator 2x-7 which can be cancelled out, yielding [1/(x²-7x+10)+[1//(x²-7x+12)]=0 Let u=x²-7x+11 [1/(u-1)]+[1/(u+1)]=0 --> u=0 x²-7x+11=0 --> x=½[7±sqrt(5)]
😊 hay que dejar claro que todos estos artificios aplicados solo surten efecto, solo si existen algunos patrones, en caso contrario, no quedará otra que PICAR PIEDRA 😊😊
Esta questão parece ser complicada, mas não é! É linda! Muito linda! Parabéns pela escolha! Brasil - Setembro de 2024. This question seems complicated, but it's not! It's beautiful! Very beautiful! Congratulations on your choice! Brazil - September 2024.
@@MyOneFiftiethOfADollar "solving this needs a lot of intuition" - However the presenter came upon the solution we are grateful to him for bringing it to us.
Yo habría usado el mínimo comun multiplo y habría resultado la ecuación como una fraccion normal.....si después me queda una ecuación de 4° grado uso Ruffini y listo....no es lo mas rápido, pero si lo mas efectivo.
Respected Vijay Sir, Good afternoon. Although there is method of solution which follows grammar of mathematics but I tried in a different way. Pls let me know this way is permitted by Mathematics or not -4=(-1)+(-1)+(-1)+(-1) So (X-10)/(x-2)=-1 X-10=2-x X+x=2+10 2x=12 X=6 2nd term X-9=3-x 2x=12 X=6 Similarly all terms produce the same same result.... Addition of t1&t4 will be (2x^2-24x+64)/(x^2-7x+10) Let a=2x^2-24x/60 b=x^2-7x+10 So the expression will be (a+4)/b...... eqn1 Again the addition of t2 &t3 will be (2x^2-24x+60)/(X^2 -7x+12) =a/(b+2).......eqn2 Eqn1 + eqn2 {(a+4)/b}+{a/(b+2)} =ab+2a+4b+8+ab=-4(b^2+2b) =2ab+2a+4b+8=-4b^2-8b 2ab+2a+8b+8=-4b^2-4b 2a(b+1)+8(b+1)=-4b(b+1) (2a+8)(b+1)=-4b(b+1) 2a+8=4b a+4=(-2b) Put the values of a & b 2x^2-24x+64=-2(X^2 -7x+10) 2X^2 -24x+64=-2x^2+14x-20 4x^2-38x+84=0 4x^2-24x-14x+84=0 4x(x-6)-14(x-6)=0 (X-6)(4x-14)=0 X-6=0 or 4x-14=0 X=6 or 4x=14 X=14/4=7/2 Hence x=6 or (7/2)
You husbands, in the same way, continue dwelling with them according to knowledge. Assign them honor as to a weaker vessel, the feminine one, since they are also heirs with you of the undeserved favor of life, in order for your prayers not to be hindered. 1Peter 3:7 see saksi ni Jehova
In the numerator and denominator x-6 missed. Hence asume x = 6
x-10/x-2 + x-9/x-3 +
x-8/x-4 + x-7/x-5
=6-10/6-2 + 6-9/6-3 + 6-8/6-4 + 6-7/6-5
--4/4 + -3/3 + -2/2 + -1/1
-1-1-1-1=-4
Thank you for the video! Very well
Explained ❤❤❤❤❤
Thank you so much for your appreciation 🙋
I used an other method.
y=x-6.
You substitute and add the first fraction with the last and add the two others. You keep the -4.
In the end, you have
(y^2-4)/(y^2+5y+4) + (y^2-6)/(y^2+5y+6) =-2. (We simplify by 2).
Let a=y^2+5y+5
b=y^2-5
We substitute, we developp and we have.
(ab+1)/(a^2-1)=-1 (We simplify by 2 again)
a^2+ab=0
a(a+b)=0
a=0 ou a+b=0
And after it is easy.
If product two numbers is zero, any one can be equal to zero. 2x-12=0, x=6.
(2х-12)=0, х=6
(1/(х-2)+1/(х-3)+1/(х-4)+1/(х-5))=0, х=3,5
15:39 The denominator can't be less than 5, so I try x = 6 and get 4 times - 1 , which is indeed - 4.
Okay, I see, 4 solutions...Nice problem!
Thanks for your valuable feedback 🌺
Each term in LHS add 1 --> RHS=0
Simplifying yields common numerator 2(x-6) which can be cancell out giving:
[1/(x-2)]+[1/(x-3)]+[1/(x-4)]+[1/(x-5)=0
Add the two terms in the middle as well as the remaning two, yielding common numerator 2x-7 which can be cancelled out, yielding
[1/(x²-7x+10)+[1//(x²-7x+12)]=0
Let u=x²-7x+11
[1/(u-1)]+[1/(u+1)]=0 --> u=0
x²-7x+11=0 --> x=½[7±sqrt(5)]
good one. but while resolving we should have compared x with 2,3,4,5 to avoid 0 in denominators.
Greetings , you explained well ,thank you we enjoyed it,.
Thanks for your valuable feedback
Very nice! Thank you.
x = 6. (= (10+2)/2 = (9+3)/2 = (8+4)/2 = (7+5)/2. Mental work, 20 sec for verifying.
Ok 👍 I agree it takes 20 seconds for verifing but not for solution
😊 hay que dejar claro que todos estos artificios aplicados solo surten efecto, solo si existen algunos patrones, en caso contrario, no quedará otra que PICAR PIEDRA 😊😊
Esta questão parece ser complicada, mas não é! É linda! Muito linda! Parabéns pela escolha! Brasil - Setembro de 2024. This question seems complicated, but it's not! It's beautiful! Very beautiful! Congratulations on your choice! Brazil - September 2024.
Thank you
7777j@@vijaymaths5483
Excellent problem with four REAL solutions! Solving this needs a lot of intuition. Thank you!
Intuition? , More probable that presenter had to look at the solution first.
Very few could solve this based on intuition.
A nice problem nonetheless.
@@MyOneFiftiethOfADollar "solving this needs a lot of intuition" - However the presenter came upon the solution we are grateful to him for bringing it to us.
Kademe, kademe anlatan, iyi bir öğretmen sınıfına giriyorsunuz. ❤👍
15:34 Excellent work
Thank you
X-10/x-2=-1. X=6 or,x-9/x-3=-1so x=6
Yo habría usado el mínimo comun multiplo y habría resultado la ecuación como una fraccion normal.....si después me queda una ecuación de 4° grado uso Ruffini y listo....no es lo mas rápido, pero si lo mas efectivo.
How to thumbnail like u?
Common denominator 60. Combine X's,, combine numerals. Am I missing something?
(X-10)/(X-2)+(X-9)/(X-3)+(X-8)/(X-4)+(X-7)/(X-5)=-4 X=7/2=3.5 X=6 X=(7 ± Sqrt[5])/2=3.5±0.5Sqrt[5]
Oh .. i was looking forward to another 15minutes of checking each of the answers by substituting into the equation lol
I like the subtitles, he speaks x-5 x-2 then two seconds of gibberish I can't discern, then again speaking math.
SENSATIONAL!
Great explanation
👏👏👏
숫자 3과 7을 저렇게 헷갈리게 쓰는 사람을 처음 보네.. 수학을 다루면서 어떻게 숫자 3과 7을 저렇게 쓸 수 있지?
И для какого класса в Америке это уравнение ?? 🤔🤔🤔🤔
В России это уровень 7 класса
Excellent
Thanks a lot 🎈
Thank you sir
Most welcome 👍
I think substitution is an easier way
X=6❤❤❤
0:50
Пишите, пожалуйста не так мелко. На телефоне не видно ❤
OK 👍 I will try my best in next time, thank you for your good suggestion ⚘️
Respected Vijay Sir, Good afternoon. Although there is method of solution which follows grammar of mathematics but I tried in a different way. Pls let me know this way is permitted by Mathematics or not
-4=(-1)+(-1)+(-1)+(-1)
So
(X-10)/(x-2)=-1
X-10=2-x
X+x=2+10
2x=12
X=6
2nd term
X-9=3-x
2x=12
X=6
Similarly all terms produce the same same result....
Addition of t1&t4 will be
(2x^2-24x+64)/(x^2-7x+10)
Let a=2x^2-24x/60
b=x^2-7x+10
So the expression will be
(a+4)/b...... eqn1
Again the addition of t2 &t3 will be
(2x^2-24x+60)/(X^2 -7x+12)
=a/(b+2).......eqn2
Eqn1 + eqn2
{(a+4)/b}+{a/(b+2)}
=ab+2a+4b+8+ab=-4(b^2+2b)
=2ab+2a+4b+8=-4b^2-8b
2ab+2a+8b+8=-4b^2-4b
2a(b+1)+8(b+1)=-4b(b+1)
(2a+8)(b+1)=-4b(b+1)
2a+8=4b
a+4=(-2b)
Put the values of a & b
2x^2-24x+64=-2(X^2 -7x+10)
2X^2 -24x+64=-2x^2+14x-20
4x^2-38x+84=0
4x^2-24x-14x+84=0
4x(x-6)-14(x-6)=0
(X-6)(4x-14)=0
X-6=0 or 4x-14=0
X=6 or 4x=14
X=14/4=7/2
Hence x=6 or (7/2)
Excellent,Thank you for sharing Manoj sir but we get 4 solutions at the end🙏☺️☺️
Thx a lot
Thank you for your feedback!
Всё мельче и мельче
X=6
Ouch! Long problem!
Long!!! But best 👌 problem
Is there is any chance that this will came in PMO
Fala língua de gente, esse trem já difícil entender em português agora vc. Imagina em grego.
Bu sorunun dört tane cevabı mı var
X=12
Vous n avez pas le droit de mettre des parenthèses
(X-12)(1/x-2+1/x-3+1/x-4+1/x-5)=0
(X-12)×k=0
K différentes de0
X-12=0
X=12.
Великолепное решение!!!❤
Thank you
What if the number is like 3,5..... somethings else and not 4?
-3y,1
Is that math olympiad 🤣🤣
Уснуть можно
What language is this fellow speaking,in between English ?.
Beautiful Indian language HINDI
@@vijaymaths5483 Okay,thanks.🤗..
X=6; x =7/2
(x ➖ 10)^2/(x ➖ 2)^2 ➖ (x ➖ 9)^2/(x ➖3)= (x^2 ➖ 100)/(x^2 ➖ 4) ➖ (x^2 ➖ 81)/x^2 ➖ 9)= {x^0+x^0 ➖ }/(x^0+x^0 ➖) ➖ (x^0+x^0 ➖)/x^0+x^0 ➖ )={x^1/x^1 +x^1/x^1}= x^2/x^2 +(x ➖ 8)^2/(x ➖ 4)^2=x^2/x^2 +(x ➖ 64)/(x ➖ 16)=x^2/x^2+ {x^0+x^0 ➖}/{x^0+x^0 ➖ }={x^1/x^1+x^1/x^1=x^3/x^3+ (x ➖ 7)^2/x ➖ 5)^2=x^3/x^3+ (x^2 ➖ 49)/(x^2 ➖ 25)=x^3/x^3+(x^0+x^0 ➖)/(x^0+x^0 ➖)={x^3/x^3+x^1/x^1}=x^4/x^4(x ➖ 4x+4) I liked loved video as aways .
In English, please? Ah fuck it ill use Mathematica
beautiful
Thanks for your valuable feedback 👍
2x _12 xuất hiện nếu Cộng thêm 1 cho các Phân số
You husbands, in the same way, continue dwelling with them according to knowledge. Assign them honor as to a weaker vessel, the feminine one, since they are also heirs with you of the undeserved favor of life, in order for your prayers not to be hindered. 1Peter 3:7 see saksi ni Jehova
Очень долго и занудно
문제를 위한 문제일 뿐입니다. 저런 문제를 만드는 사람은 할 일이 전혀 없는 무가치한 사람임이 틀림이 없습니다. 창조적인 것에 시간을 쓰세요!
Excellent
x=6
x=6