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Challenge ! Can You Solve This Quadratic Equation ?
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- čas přidán 26. 07. 2023
- In this video we will use a non-standard method to solve this Special Quadratic Equation.
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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 ❤
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
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 😂
😂
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
👏👏
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
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 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
The question can also be done by comparing factors on both sides in very convenient way
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 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
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?
@@Movie-MOVlE 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
Kudratic equation
Dill choo jata hai sir❤
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
@@MathsandScienceTutorialsYT 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)
Your explanation and question approach is superb sir ✔️
I do it simply by calculator
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❤
Sir ek bar kardo na moment of inertia standard geometry ke derive using integral calculus please. 🙂
Ekdam BHANNAT
well done u r simply genius
Fantastic question sir
Dimag ke dhage khol diye
Sir is teaching us in Pathfinder barasat
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
अदभूतम्❤️💫🌟
Super guru ji ..kya sawal tha yaar hila dala...
Bhannat
4 aur 2 ke saath jo aapne kara na sir vahi maine bhi kiya starting mein😮😮
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 :)
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 😂😂😂
i solved this in about 15 minutes with the quadratic formula
🔥🔥🔥🔥
Kya baat hai sir ek dam mast...❤
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.
Sir plz application of derivatives ka aakhri lecture daal do humble request sir
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.
Best approach thnks sir
phenomenal sir
Very nice method of solving sir
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) !
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
Sir u r just awesome, you break the concept to the basics, that makes you the most
You are the best maths teacher , I have ever seen on youtube❤
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.
Sir Please have a Video on Convertendo,, Invertendo,, Alternendo, Addendo 😢😢😢
@5:57 "badmaash..."...😂😂
I solved it
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
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 please solve this question 12x^4 - 56x^3+89x^2 -56x +12
you have a great approach to problem solving
Mast question thaa sir
Nice sir mja aa gya
Lajaawab question aur waisi hi lajawaab solution
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 😅
👍👍 Wow Sir, THANKS So much for giving us a new thought !!! Keep Bringing these videos pls .
Sir, mera method alag tha magar answer sahi aaya. ❤
I solve this question in first attempt
Sir you could also solve this question by comparison
a(a+1) = 6p(6p+1)
Then we get a=6p
And the second solution can be
a=-6p
We had basically have got a positive pair and a negative pair of the same number which is
(6p, 6p+1) and (-6p, -(6p-1))
As negative into negative always gives us positive and hence here are the two solutions of this quadratic equation .... There you dont even have to apply the roots formulas and all it can be solved via just basic knowledge of maths
And also there was only one and such pair of two consecutive number which gives us 44444442222222 therefore there will be only i pair but just the positive one and the negative one
Maths best teacher
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.
mind blownn 😊
Sir awesome
Hats off sir
Jadu Jadu...❤❤❤
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
You are a great teacher sir. Please make videos on previous year jee maths questions.
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 I believe we can directly write a(a+1)=6q(6q+1)
And then a=6q
I believe it would be easier
Yes
a * (a+1) = (6q) * (6q+1)
and
a * (a+1) = (-6q -1) * ((-6q - 1) + 1)
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
Sir I solved it in 5 minutes...I saw the sequence of 42=6*7 then 4422=66*67 and then so on....
Sir if we divide individuals by a then also we can get same answer??
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
Excellent sir
Sir 8:31 pe a²+a ko a(a+1) rkh ke lhs rhs ko compare kr de i mean a(a+1) =6p(6p+1) that is a=6p
Can't we just use the quadratic equations formula, (-b+/-√(b2-4ac))/2a
I got it by that easily
Nice question made it to third step but confused what combination to use for 10000000....i qas trying 8888888 + 2222222 but if i kept in mind that i had to make something like a^2 + a...i would have got it🤦♂️...very nice question for combining terms
Answer was done at 5:30 itself. a(a+1) =6p (6p+1). a=6p. a=6666666. For every such equation where a^2+ a = X , if one root is m, 2nd root is -(m+1).
Cudratic equation
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
Short tick
Split the number in 2 parts 4444444 and 2222222
Then then add them
6666666
tf are you tryina do?
What kuch bhi😑
Cudratic ,kudratic equation
Mainai toh 5:22 pe equation ko dekhle a=6p assume kr liya by comparison 😂
Aman sir is looking like thugess
Sir ji question bhut hard laga but aapna sumjhaya tho easily sumajh m aagya 😊
You are amazing sir....God Bless you !!
Sir please solve x^x=2
Fantastic.
Sir aapne isse pehele ek Olympiad ka question liya tha usme bhe itne bade numbers the to apne ke pattern se bhi solve Kiya tha end so mene bhi yahi socha and then I came up with..
6*7=42
66 * 67 = 4422
666 * 667 =444222
66... n times * 66... (n-1)times 7 = 444... n times 222... n times
Sir mein aise karta
a2+a=6p(6p+1)
a(a+1)=6p(6p+1)
Either a=6p or a+1=6p+1
Then you can't get the negative solution
Sir please can you make video on first and second derivative test.....maxima and minima part 2(application of derivatives)
Yhi chiz unique bnati h maths ko har qs ka solve hone ka apna tarika hai logic se nhi chalta aksar
Sir but I got the ans without doing solution in copy just done by mind and was correct 🙃
Sir maine khudse try kiya aur bina apka solution dekhe jab mera answer aaya toh bahut maja aaya
Sir please make a video on ivertendo
Sir golden ratio aur devil number par bhi ek video banaye please🙏🙏
Love this question
LHS : a^2+a ko a(a+1) likh sakte ... mtlb do consecutive terms ka product RHS : 44444442222222 mein se 2222222 common le toh -> (2222222)(20000001) milega prr Hume do consecutive no. Ka product ke form Mai Lana hai toh (20000001)>(2222222) 20000001 is greater than 2222222 issi liye 20000001 ko factor krrke 2222222 se multiply karwana padega we can write 20000001 as 3×6666667 aur shift krrne pe (6666666)(6666667) = a(a+1) mil gaya format aur -ve sign laga krr dusra value bhi nikal sakte
That was
BHANNAT!!!!!💯💯💯💥💥💥
Loved it kudretic eqn❤
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
True man uses quadratic formula
kudratic equation