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
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
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.
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
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
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❤
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
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
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
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 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
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 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.
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
@@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)
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 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
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
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
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
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
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 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
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
👏👏
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
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 😂😂
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❤
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 😂
😂
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
Your explanation and question approach is superb sir ✔️
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 😂😂😂
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
Very nice method of solving sir
Sir ek bar kardo na moment of inertia standard geometry ke derive using integral calculus please. 🙂
Ekdam BHANNAT
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.
you have a great approach to problem solving
Best approach thnks 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
phenomenal sir
Sir if we divide individuals by a then also we can get same answer??
Sir u r just awesome, you break the concept to the basics, that makes you the most
Super guru ji ..kya sawal tha yaar hila dala...
Bhannat
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 😅
sir quadratic formula se easily solve hua hai very easily ek baar ap attempt dijiyega :)
Fantastic question sir
Dimag ke dhage khol diye
Sir is teaching us in Pathfinder barasat
Sir Please have a Video on Convertendo,, Invertendo,, Alternendo, Addendo 😢😢😢
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 please solve this question 12x^4 - 56x^3+89x^2 -56x +12
Sir plz application of derivatives ka aakhri lecture daal do humble request sir
Kudratic equation
Dill choo jata hai sir❤
Sir cengage book ke question nahi soch pa raha how to do
well done u r simply genius
Can't we just use the quadratic equations formula, (-b+/-√(b2-4ac))/2a
I got it by that easily
Excellent sir
You are a great teacher sir. Please make videos on previous year jee maths questions.
Fantastic.
Lajaawab question aur waisi hi lajawaab solution
अदभूतम्❤️💫🌟
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 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
4 aur 2 ke saath jo aapne kara na sir vahi maine bhi kiya starting mein😮😮
Kya baat hai sir ek dam mast...❤
You are the best maths teacher , I have ever seen on youtube❤
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).
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)
👍👍 Wow Sir, THANKS So much for giving us a new thought !!! Keep Bringing these videos pls .
Nice sir mja aa gya
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 I solved it in 5 minutes...I saw the sequence of 42=6*7 then 4422=66*67 and then so on....
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.
You are amazing sir....God Bless you !!
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.
Maths best teacher
Hats off sir
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
Sir please make a video on ivertendo
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
Sir awesome
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)
Jadu Jadu...❤❤❤
Mast question thaa sir
Cudratic ,kudratic equation
I solved it
Love this question
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
I see all your videos and I want the question like it by u....❤❤❤❤❤❤❤❤❤❤
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
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 golden ratio aur devil number par bhi ek video banaye please🙏🙏
I do it simply by calculator
Nice question
Sir maine khudse try kiya aur bina apka solution dekhe jab mera answer aaya toh bahut maja aaya
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
Sir ji question bhut hard laga but aapna sumjhaya tho easily sumajh m aagya 😊
Kaya crack ha sir ❤
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
Great
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
🫡🫡 5:40
Nice aproch😇😇
Sir please can you make video on first and second derivative test.....maxima and minima part 2(application of derivatives)
Shaandar🎉🎉😮🎉🎉❤
That was
BHANNAT!!!!!💯💯💯💥💥💥
Sir please make a video on zeroth root of x
Blown🤯🤯🤯
Sir What is the meaning of bhannat?
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
Use sequence series and then try
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, mera method alag tha magar answer sahi aaya. ❤
Sir please solve x^x=2
@5:57 "badmaash..."...😂😂
Very nice
Khatarnak
Loved it kudretic eqn❤
Similar concept qus in jee advanced 2023
Sir mene basic se Kara hai 10 min mein ho to gaya per aapka thought processes kya hai uske liye aaka vedio dekh rahe hai ❤
❤❤