Challenge ! Can You Solve This Quadratic Equation ?
ฝัง
- เผยแพร่เมื่อ 29 ก.ย. 2024
- In this video we will use a non-standard method to solve this Special Quadratic Equation.
Subscribe to @BHANNATMATHS for brain-twisting videos around maths.
========================================
🚀🚀Social Media Links:🚀🚀
----------------------------------------------------------------------------------------
Telegram: (Channel) - t.me/bhannatma...
(Group) - t.me/bhannatmaths
Telegram Handle: @bhannatmaths @bhannatmathsofficial
Instagram: / mybhannatmaths
Twitter: bh...
----------------------------------------------------------------------------------------
#quadraticequation #amansirmaths #maths #bhannatmaths
For any query/doubt mail us at: bhannatmaths@gmail.com
For All Notifications Join Our Telegram Group: @bhannatmaths
sir i observed a pattern
6x7=42
66x67=4422
and so on
so (6......6) x (6......7) = 44444442222222
and so we cen write it as
6.......6 x (6......6 + 1) = a(a+1)
so we get a= 6666666 or a= -6666667
yeah!
that's too a good method.!
Best soln
Cool solution !
Amazing mann
Good approach ❤
I'm in class 8th but I love seeing your videos.I understand,not fully but yes I understand 😊
Keep it up son. Way to go. Maths is next to God
I am in 6th class😂😂😂😂
To hum kya kare
I am in nursery 😂
😂
Sir we can also get the answer by comparing a^2+a = 36p^2+6p , and 36^2p aslo can be written as 6p^2 now, we can get the answer by comparing both sides which will give the value of a is 6p
Yes I also did like this
Sir, maine socha ki kyu itna bada number se deal krna hai apan pehle chote number per dekhte hai toh maine equation maana a^2 + a = 42 jaha se maine isko likha aise a(a+1) = 42 isme a =6 satisfy kar rha hai phir maine a(a+1) = 4422 ko dekha toh ye 66 ×67 hai phir pattern ka pta chal gya toh iss waale question ke liye a = 666...7times ans ajaayega aur dusra root -b/a = sum of roots se aajaayega.
Btw love your explanation❤
The unit digit of 'a' can be 1, 6 or 8 only, as the unit digit of eq value is 2. Seeing the eq value 6^2 +6 =42, also 66^2+ 66 =4422 hence a= 6666666.
Sir mera bhi aap jaisa method tha bas us equation pe aane ki approach aisi thi ki
Pehle pattern observe karne pe ye dikha this type number can be written as
2(10^7-1/9-2[10^14-1/9 - 10^7-1/9])
Where we can let 10^7-1/9 =p
Hence that same quad equation can be formed
a^2+a=36p^2+6p
a^2+a=(6p)^2+6p
On comparing
a=6p
And we take p=1111111
a=6×1111111
=6666666
Sir cengage book ke question nahi soch pa raha how to do
sir quadratic formula se easily solve hua hai very easily ek baar ap attempt dijiyega :)
well done u r simply genius
I do it simply by calculator
Sir maine to pehle 42 leke eq solve ki fir 4422 leke solve ki to pattern mila
(-1+-13) /2 and (-1+-133) /2
So maine direct answer likh diya (-1+-13333333)/2
Sir plz application of derivatives ka aakhri lecture daal do humble request sir
you have a great approach to problem solving
@5:57 "badmaash..."...😂😂
I solve this question in first attempt
Solved that in 30 seconds, but used calculator in handling big number, and not used the standard formula.
Yhi chiz unique bnati h maths ko har qs ka solve hone ka apna tarika hai logic se nhi chalta aksar
Nice sir mja aa gya
You are amazing sir....God Bless you !!
Excellent sir
First treat the special number 44444442222222 = 6666666 x 6666667 ---> n(n+1) = n^2 + n
----> a = 6666666
Now let’s understand the number 42 = 6x7
4422 = 66x67
444222 = 666x667
…
…
…
Here we can use a clever pattern (conjecture) not here I am claiming By principle of mathematical induction.
I have used a simple formula for solving this problem 42=6*7,4422=66*67 so like 44444442222222=6666666×6666667
It also happens with 3 and 4 number
Ye bahut mushkil sawaal h
Issey to Koi bhi solve nhi kar sakta Pehli baar me jab tak k wo solution na dekh le
Shaandar🎉🎉😮🎉🎉❤
c²
If , 6×7 = 42 & 66 × 67 = 4422
Then , we can conclude that 666 × 667 = 444222
[ Sir,I have that please understand the pattern of multiplication and it's answer]
Therefore,6666666 × 6666667 = 44444442222222
a^2 + a = 6666666 × 6666667
a(a + 1) = 6666666 × (6666666 + 1)
Now,let y be 6666666
.•. a(a + 1) = y(y + 1)
.•. a^2 + a = y^2 + y
.•. a^2 - y^2 + a - y = 0
.•. (a + y)(a - y) + 1(a - y) = 0
.•. (a + y + 1)(a - y) = 0
.•. a + 6666666 + 1 = 0 OR a - 6666666 = 0
.•. a = - 6666667 OR a = 6666666
Sir, Is this a correct way to solve this question
And I tried this question and I solved it like this.
Sir shreedhracharya se bhi bhut jldi aa raha hai
Answer is -66,66,667 and +66,66,666
With
11×101=1111
111×1001=111111
Then I did 111×2001=222111
Then, 4002×111=444222(3 times 4,3 times 2)
Then,for 7 times 4 and 2
7 times 2 I took 1111111
So, I tried 4002×1111111 = not getting suitable results...but during this multipliplication I realised that 4002 will not work, so I starting putting zeros from left(4002) which become 40000002
So, 40000002×1111111=44444442222222
now write 40000002=2×20000001
Multiply this 2 on 1111111
We get 20000001×2222222 (2crore1×22lakh)still very far from getting +1(because in middle term spiiting, i need +1a....as the eqn is a^2+1a-44444442222222)
Then I realised 20000001 is divisible by 3
So write 20000001=3×6666667
Multiply this 3 on 2222222
I.e. 20000001×2222222=6666667×6666666
Whos difference is +1
Hence,a^2+a-44444442222222=0
a^2+6666667a-6666666a-6666667×6666666=0
a(a+6666667)-6666666(a+6666667)=0
(a+6666667)(a-6666666)=0
therefore,a= - 6666667,6666666
I like your vedios
Please pronunce quadratic correctly.
TALENT OF AMAN SIR, = GOLD MEDALIST IN MATHS
Hatt bc😂😂 InMO mei aise nhi hota ye toh like general pattern recognition tha jo ki sort of relevant hai ioqm mei but mixed concept
I am in LKG ..... watching this at 1.75x
👎👎Solution could have been done smaller than this
You just increased the steps by making roots of that equation
Answer was completed on the 1st slide
a²+a=6p(p+1)
a(a+1)=6p(p+1)
Comparing a=6p
Sir...I solved it in other way❤😊
How did u solve it
@@rexkarim7-zt2lp yes....phle42 ko lekr..tb ans 6 Aya........fr 4422 ko lekr tb ans66 Aya.... fr 444222 ko lekr.. tb ans...666....pattern..smjh a gya....so finally ans 6666666 aya
Good approach. Shortcut
@@rexkarim7-zt2lp thanx ❣️
I solved by finding square root of 44444442222223 lmfao
Why
My solution: a^2+a=a(a+1)
42=6*7
4422=66*67
444222=666*667
Hence by pattern
44444442222222=6666666*6666667
Hence a=6666666
Also
44444442222222=-6666666*-6666667
Hence a=-6666667
I didn't notice the negative solution but after seeing sir's solution I noticed that there were 2 solutions
Yes 👍
I used quadratic formula and got same answers 😂😂
a(a+1)=6p(6p+1) we can directly write a=6p
Now for the second root α+β = -b/a i.e α+β = -1 can be used. Really nice question
Thanks bro, I used the same method. But i was stumped when i couldn't figure out the second root.
Could you explain me how you did the first step?
Bro m bhi yahi soch Raha tha
@@Just_someone_out_hereby comparing both sides
same
In such questions, many a times pattern is the shortest way. a(sq) + a=a(a+1). Pattern: 6×7 =42 ,66×67=4422 so number of 6 in 66 is number of 4 in 4422. So solved
Same
👏👏
Aman sir is looking like thugess
I used the method of comparision :
a²+a=6p(6p+1)
=> a(a+1)=6p(6p+1)
by comparision, a=6p.
But that gave me just one root. Then I saw a comment here saying the same thing but he also used x1+x2 = -b/a.
So, 6p+x2=-1
=> -(6p+1)= x2.
This was an amazing question.
Absolutely
Please make a video on comparing e^pi and pi^e, an interesting question
Also first one here
Aod se ho jayega vo
Take a fx = x^(1/x)
Iska maximum value e pe aati h
Fir bs normal inequality hoti h
It can be solved using monotonicity
Assume a function f(x) = x^(1÷x)
Now proved that this is an decreasing function
Now e f(π
e^(1÷e) > π^(1÷π)
e^π>π^e
Use lnx/x function
Sir mene aapse bhi jaldi kardiya,
Mene 44444442222222 ka directly cube root le liya, jo 6666666.5 aa raha tha, fir mene 6666666 and 6666667 ka multiplication kiya to 44444442222222 aa gaya, fir kya 44444442222222 ke do factor mil gaye jinka subtraction kare to 1 aata hai.
a(a+1) = that number
i.e., 2 consecutive integers
Take sqrt of that number, it is 6666666.4999
So your numbers are 6666666 and 6666667
Also their negatives will also be soln
Koi itna kaise gir skta hai..basic science academy ne 1 month phle is question ko solve kiya tha h aur inka bhi vahi approach..bhai khud ka content Lao kb tk chori ke content se chaloge...
Us Buchare ke pas sirf 550 subscriber h are yar km se km question post krke cmt me solution ka link dal dete..
I observed the pattern of 6 square +6=42
66 square +66=4422
And so on and found 6666666 ass root and found other root by sum of root.
Mainai toh 5:22 pe equation ko dekhle a=6p assume kr liya by comparison 😂
Kudratic equation
Dill choo jata hai sir❤
Sir you did so much in last step we can simply do a²+a=6p(6p+1) = a(a+1)=6p(6p+1). (by comparing) 6p=a
But we are not getting second value of a i.e -(6p+1)
@@rk-blogs552U can by using alpha and beta method, the last part was complicated on purpose so that we would learn how to factorize
4 aur 2 ke saath jo aapne kara na sir vahi maine bhi kiya starting mein😮😮
Sir we can solve from this
a2 + a =44444442222222
We can write,
44444442222222=44444444444444-2222222
=6666666^2 + 8888888-2222
222
=6666666^2 + 6666666
Then a=6666666
i solved this in about 15 minutes with the quadratic formula
🔥🔥🔥🔥
Sir ek bar kardo na moment of inertia standard geometry ke derive using integral calculus please. 🙂
Big fan sir !! you always help us to improve ourselves !!
yes, he is the best maths teacher I have met ever
@@MrDADYSingh you met him?
@@hhsyw on youtube, she means
@@capsteverogers hey hai captain
i observed a pattern
6x7=42
66x67=4422
and so on
so (6......6) x (6......7) = 44444442222222
and so we cen write it as
6.......6 x (6......6 + 1) = a(a+1)
so we get a= 6666666 or a= -6666667
Who all thought this is just useless question 🤡
This problem is too easy sir when I saw this problem I was shocked that what is this but when I took pen 🖊 and paper and with the kripa of God I solved the first attempt and in this problem a great observation that is made his deffirent question than the others. That's why 😅the unique problem of quadratic equations.
a=-6666667 , a=6666666
what i did to solve this is
i first square rooted the number.
got 6666666.5
i took 6666666 and squared it.
then i added the same number 6666666
i got the answer easily - 44444442222222
try it.
For any number with 2n digits if first n digit is consecutive 4 and next n digit is consecutive 2 then let the number is d then a^2+a=d has a solution with a=6666...6(where the number of 6 in a is n). We can prove this by induction. Also then other root a Can be found by factorization that is a^2+a-d=(a-66666...)(a-k). Then k+6666...6=-1 then k is -666...67 but also we need (66666..)×k=-444..4222..2.
Thus the solution of a is a_1=666...6 or a_2=-6666...67 where in a_1 there are n 6's and in a_2 there are n-1 ,6's and last digit is 7
My method:-
Hit & trial:- 6^2+6= 42 (looks similar to give pattern)
Then try 66^2 + 66 = 4422
Now it is confirmed ☺️,
Answer is :- 6666666
6666666^2 + 6666666 = 44444442222222
&
For 2nd answer:- (-7)^2 +(-7)=42
So, similarly answer is:-
-6666667
😂 it's so easy bro use trial and error method
Use unit digit metho everything why this much effort
Like this
a(a+1) form
Use numbers
3×4=12 it doesn't follow the answer
So use
6×7 =42
So it follows
So X = +/- 6666666
I.e = 6666666(6666666+1)=
6666666×6666667=44444442222222
It's easy if you do it in mind it can be done under 10 sec easily
Tried solving it by distributing as 4*10¹³+4*10¹².......4*10^8 + 2*10^7+....2*10²+2
Then taking common,, the question was getting simplified afterwards though but,, didn't had the courage to go on as it was being like 10^7*(1-10^6) / (10-¹ - 1).. (was solving the number part, what I wrote here was just the part that was getting complicated) !
Hamesha calculation control me nahi rehta hai. Kuch problem some unique technique se solve hota hai aur boh yad bhi rakhna parta hai. Aisa situation me hamesa concept kam nahi karta hai. Am I right dear viewers?
Sir I solved it in 5 minutes...I saw the sequence of 42=6*7 then 4422=66*67 and then so on....
Short tick
Split the number in 2 parts 4444444 and 2222222
Then then add them
6666666
tf are you tryina do?
What kuch bhi😑
Or we can driectly take. 2222222 common from. First step then we get factors as 6666666,-6666667
Direct lagao Quadratric, kaha sir matha kharap karte ho bacho ka....khud kahi se dekh k kya... Kya control?
Formula lagaao do min me aayga
एक्शन देखते हैं मुझे समझ में आ गया tha ki a ki value 666666 hoga.
Fantastic question sir
Dimag ke dhage khol diye
Ye question kon sa exam puchha hai sir g....agar puchha bhi hai to skip karke jaana chahiye nahi yahi questions me dimag lagate lagate pura exam khatm ho jayega jab aapse 6bse 7min lag raha to hum sab or samay lagega
Sir at 4:06 there's a mistake
There should be 6 ones so that there would be 7 zeroes,but you have taken 7 ones then there will be 8 zeroes and we cannot take that as p and hence the answer would be wrong.
Sir please solve this question 12x^4 - 56x^3+89x^2 -56x +12
Sir maine toh shuru Mai hi Shri dharya Chari formula use krdiya aur answer bhi shi agya lekin bas square root nikalne mei thoda jyada time lag gya
Sir is teaching us in Pathfinder barasat
Sir, mera method alag tha magar answer sahi aaya. ❤
Sometimes after copying the question, I get stuck in the very first step, 😢
Agar formula laga ke karte to aajata but root of 177777768888889 nikaal ne mei dikkat ho jati
I am in class 8 an aspirant for IOQM and also i have solved this equation but only one
Yaar mai gadha pehle step mei shridhacharya use karke 10 min calculate karke ans nikala, sir ne ek second mei kar diya
Sir but I got the ans without doing solution in copy just done by mind and was correct 🙃
a=6666666 and a= -6666667, I solve it pausing this video...really...
Your explanation and question approach is superb sir ✔️
Ekdam BHANNAT
Matlab if we take a variable 'a' and a constant 'z' such that (a)^2 +a = (z)^2 +z, the value of 'a' can be a = z or a = -z-1...putting both of these value will give (z)^2 + z
@SAKSHAM-kz2qi 😂😂😂
Same dialogue like 100 times. That's the equation.
5:21
Sir,
isi step mein pehla solution agaya sir
a²+a=(6p)²+6p
So a=6p.
Please check this Sir.
🙂
it is only one solution for a but there will be two since it is quadratic
@@MathsScienceandHinduism yes just thought about it .
that gives only one factor, sir is not a fool, he knew it but shown us proper 2 factors factorization step useful everywhere
@@MrDADYSingh 👍👍
@@Huzzugamer2005 nhi i bas yhi pair banega iske ilava nhi ban skta agar banega toh uska simplification yhi hoga- jaise a(a+1)= 6p(6p+) so there is only two possiblities
a= 6p or a= -(6p-1) by this -1 is cancelled and and whole product becomes +ve and second product becomes (6p+1)
Why can't you write
a(a+1) = 6p(6p+1)
So a= 6p
0r a = 6666666
Sir calculator se quadratic formula lagaya aur answer aagya😂😂😂
🫡🫡 5:40
Similar concept qus in jee advanced 2023
Sir Please have a Video on Convertendo,, Invertendo,, Alternendo, Addendo 😢😢😢
Speak less, solve more. Dont waste time in commentary.
a^2 + a = 44444442222222
Notice that there are seven 4s followed by seven 2s, hence 2222222 has to be a factor
a^2 + a = 44444440000000 + 2222222
a^2 + a = 4444444 * 10000000 + 2222222
a^2 + a = 2222222 * 2 * 10000000 + 2222222
Factor out 2222222
a^2 + a = 2222222 * (20000000 + 1)
a * (a + 1) = 2222222 * 20000001
Since we are looking for factors a and a+1 and a is going to be a very large number, a ~= (a+1) so we are looking for something close to a square root of RHS
Notice that second factor (20000001 ~= 2 * 10^7) is approximately 10 times larger than first factor (2222222 ~= 2.2 * 10^6), and sqrt(10) is slightly more than 3. Hence we can factor out a 3 from the second factor and multiply it into the first one to get something closer to the actual answer.
a * (a + 1) = (2222222 * 3) * (20000001 / 3)
a * (a + 1) = (6666666) * (6666667)
a * (a + 1) = 6666666 * (6666666 + 1)
a = 6666666
OR
a * (a + 1) = (6666666 * -1) * ((6666666 + 1) * -1)
a * (a + 1) = (-6666666) * (-6666667)
a * (a + 1) = (-6666667) * (-6666666)
a * (a + 1) = (-6666667) * (-6666667 + 1)
a = -6666667
Sir if we just add the 4444444 and 2222222 we will get the same answer
5:22 Aap yahan par a2+a=36p2+6p ko direct a2+a = under root (6p)2 +6p compare kar skte the..
a=6p (p=11111111)
And a=666666 ans.
Maine vi yehi socha tha 😅
Kudratic equation 😂😂 but nice explanation
I solve without doing this very easy question
Abey dhang se bolna toh seekh le kuudratic kya hota h
a(a+1) = 44444442222222
a(a+1) = 6666666(6666666+1)
So a = 6666666
Got only first answer not able to get the second one 😔
Multiple of 2 consecutive numbers