How To Solve An Octic Equation? | Solving Amazing Octic Equation | Aman Sir Maths

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  • Опубліковано 26 гру 2024

КОМЕНТАРІ • 204

  • @cascabellah
    @cascabellah Рік тому +78

    Me : it's scary
    Sirji : it's beautiful ❤️💕

  • @ratnabhasati2249
    @ratnabhasati2249 Рік тому +16

    Sir mazaa aa gaya.. this is one of the best questions I have ever solved… sir please bring more videos like these.. I really love your videos 😊😊

  • @randomjudgements8852
    @randomjudgements8852 Рік тому +2

    1 is a root
    As sum of coefficients is zero

  • @ajitkumarverma2403
    @ajitkumarverma2403 Рік тому +1

    Sir last me mja aa gya. Bilkul bhannat tarike se.

  • @joc4970
    @joc4970 Рік тому +3

    so what we did is we converted fractional expressions to reducible forms so that it can be easy for us to solve. nice

  • @yugahuja2303
    @yugahuja2303 Рік тому +5

    5:42 amazing dance 😂😂😂😂😂

  • @dragonslayer7364
    @dragonslayer7364 Рік тому +1

    Zeher sir maja aa gaya mujhe toh bahut mushkil lag raha tha lakin aapne ekdum easy way mein samjha diya

    • @MathematicalPool
      @MathematicalPool Рік тому

      Kya kabhi koi dusra questions kar paoge?

    • @dragonslayer7364
      @dragonslayer7364 Рік тому

      @@MathematicalPool of course agar isse similar hoga tab kyon ki 10 wagera mein maximum power 4 tak hi questions padhaye gaye hai

    • @MathematicalPool
      @MathematicalPool Рік тому

      @@dragonslayer7364 10th me 4 degree padh liye ho???????? Kaha se ho bachche??

  • @amits4744
    @amits4744 Рік тому +20

    There are Mathematics channels like 3Blue1Brown, Mathologer, Black pen red pen, etc in UA-cam. This channel can become a popular Mathematics channel from India as Sir looks interactive when teaching

    • @TechnoCoderz369
      @TechnoCoderz369 Рік тому +1

      Only if sir teaches in english

    • @amits4744
      @amits4744 Рік тому

      @@TechnoCoderz369 why english. Why can't we have channels like 3Blue1Brown, Mathologer, Black pen red pen, etc in hindi

    • @samarpitasaha3855
      @samarpitasaha3855 Рік тому +5

      @@amits4744 Because not everybody knows Hindi🙄

    • @HUNTER-qn5ff
      @HUNTER-qn5ff Рік тому +4

      ​@@amits4744 Hindi is not a universal language so that is why we should speak in English

    • @JEEADV-x7g
      @JEEADV-x7g Рік тому +2

      @@amits4744 entire world uses english. Its not anti-patriotism for you to accept this fact😭. Indians really be defending India in everything lmao

  • @KoolaidGuys
    @KoolaidGuys Рік тому +1

    quadratic equation❌
    Kudratic equation✅

  • @user-unkn0wn444
    @user-unkn0wn444 Рік тому +4

    Bohot accha samjhaya hai aapne 🔥🔥

  • @pranavmishraYT
    @pranavmishraYT Рік тому +1

    ❤ really love your videos sir,,,plz ese video laate rahiye jisme question ki approch discuss ho..❤

  • @AmanYadav-ob5hr
    @AmanYadav-ob5hr Рік тому +16

    Sir you are brilliant 👍😎 and your teaching style is very unique to all 🙏🙏 you are legend sir 🤓🤓

  • @biswaranjan17
    @biswaranjan17 Рік тому +26

    Sir please start teaching us BSc and engineering mathematics it will help us a lot. your teaching style is so unique sir🙏 when I was in 11th and 12th I studied maths from your videos and I always love to see your videos sir your all videos are amazing and loving.🤍♾️🙏

  • @fitnessguru34wala
    @fitnessguru34wala Рік тому +4

    Sir really maja a gya first time mathematics ki itni large equation ko solve karnai mai so love you sir for that struggle

  • @ajayshankermanitripathi9590
    @ajayshankermanitripathi9590 Рік тому +3

    Sir its very kind of you to help us for so long without any charge

  • @thepi553
    @thepi553 Рік тому +1

    How to find the height of any triangle when side length is given. I mean that if any triangle's side is a, b and c then what will the height be of this triangle.............🤔. Is there any formula, by using that we can find the height of any triangle........

    • @advaykumar9726
      @advaykumar9726 Рік тому

      Find the area by herons and divide by base

  • @VrajShah-fy4zc
    @VrajShah-fy4zc Рік тому

    5:43 Sir aa gayi baat samajh mei :)

  • @aryanrawat5961
    @aryanrawat5961 5 місяців тому

    Sir ye to ek dum starting mei hi hit and trial se ho raha tha maine bhi pehle 1 daala phir 2 aur ho gaya solve. 1 minute bhi nahi laga. Maana x=2 ki calculation bohot heavy hai par phir bhi ek baar calculation karlo to bohot jaldi solve ho raha hai pura question.

  • @mirzamahboob7903
    @mirzamahboob7903 Рік тому

    You can use pascal triangle for roots of t atleast

  • @bgmigamerz74
    @bgmigamerz74 Рік тому +1

    Mind blowing 🤯😲

  • @pritamkumar-qe5vm
    @pritamkumar-qe5vm Рік тому

    Hit and trail method ko chhod kr kya koi dusra method n use kr skte hai?

  • @subhashpatil2833
    @subhashpatil2833 Рік тому

    Sir outstanding.🙏🙏

  • @physicscity_
    @physicscity_ Рік тому +2

    Fantastic Sir love you sir ❤️

  • @ashwanibeohar8172
    @ashwanibeohar8172 Рік тому

    Trial and error with x=1, and x=2 can be tried just after dividing by x^4

    • @TheArchit1
      @TheArchit1 Рік тому

      but how will you find other roots? for that you have to reduce it to a 4 power equation

  • @ujjwal5460
    @ujjwal5460 Рік тому +40

    To be honest As a MSC maths
    I could easily tell that solving every octic isn't possible
    Is it bcz QUINTIC EQNS KA KOI FORMULA NHI BANA BS QUARTIC KA HOTA H JO KI MERE TAK KO BHI SMJHNE ME HALAT KHRB HOGYI NO ONE USES IT ...ITS TRASH TBH😂😂😄🤣🙂😑

    • @e_pi_i_is_-1
      @e_pi_i_is_-1 Рік тому +7

      Neither is any equation with degree of polynomial more than 5
      (Only possible if u use computer)

    • @sleha4106
      @sleha4106 Рік тому

      ​@@e_pi_i_is_-1Galois Theory

    • @ujjwal5460
      @ujjwal5460 Рік тому

      @@e_pi_i_is_-1 bhai bhai 5th ka bhi formula nhi hota bro or aage ka to bilkul nhi

    • @e_pi_i_is_-1
      @e_pi_i_is_-1 Рік тому

      @@ujjwal5460 you can deviate the formula just like u deviate the formula for quadratic equations.
      Only thing is that, it would take up like 10 pages of register.
      The cubic formula takes one a4 sheet

    • @MathematicalPool
      @MathematicalPool Рік тому +1

      @@e_pi_i_is_-1 ye proof ho chuka hai 4 degree ke baad aap solve nahi kar sakte hai

  • @soumyadeepBindhani...
    @soumyadeepBindhani... Рік тому +1

    Sir mujhe itne achhe lagte ho ap kya hi bolu main . Mera fav sub bhi mathematics hai . Isliye main apka har ek video dekhta hun kuch neya sikhne ka liye

  • @nagasaiprajith2302
    @nagasaiprajith2302 11 місяців тому

    Very easy question tha sir..❤

  • @doraemon2386
    @doraemon2386 Рік тому +2

    Sir I have a request.. please make a video on 'Descartes Rule of Sign'.. please sir, before JEE starts 🙏

  • @shubhankarmahashabde1029
    @shubhankarmahashabde1029 Рік тому +1

    Sir isko x - 1 se divide karke bhi solve kar sakte the na?

  • @KuldeepSharma-cv3nn
    @KuldeepSharma-cv3nn Рік тому +1

    Sir : app video pause karke apna attemp lagaye
    Me : mera attenpt toh thumbnail dekhke hi pura ho gaya tha

  • @raouf369
    @raouf369 Рік тому

    You ar amazing sir.❤

  • @jayprakashverma4529
    @jayprakashverma4529 Рік тому +1

    Sir function x²+2x+1/ x² - 8x+12 ki range Bata dijiye

  • @Physicslover1729
    @Physicslover1729 Рік тому +2

    Learned something new sir ♥️♥️♥️

  • @vaibhavmevada9668
    @vaibhavmevada9668 Рік тому +1

    Sir aap amizing videos ki playlist bana do na please

  • @jeeteshsingh1840
    @jeeteshsingh1840 Рік тому

    Sir aur koi condition ya coefficient pe octic equation solve kareya kyoki
    Iska 8 Zeros ayega
    Aur sir aise question ko put up kariye jiske zero irrational bhi ho

  • @faysalrahman9493
    @faysalrahman9493 Рік тому

    Sir, do we have any simple solve of octic equation like quadratic one.

  • @Mathsloverr
    @Mathsloverr Рік тому +2

    Sir I love you, u r my inspiration 😊🙏🙏

  • @akashhalsa3262
    @akashhalsa3262 Рік тому +1

    Reciprocal equation

  • @Questionpartice
    @Questionpartice Рік тому +2

    Sir u r amazing sir

  • @mohitsharma8067
    @mohitsharma8067 Рік тому +2

    Sir please start class 11 maths. Our board exam was over

  • @abhaychauhan4950
    @abhaychauhan4950 Рік тому +5

    Jo bhi Aman sir ko pasand karta ho like karooo❤❤❤❤❤❤

  • @anuragsinghtomar1130
    @anuragsinghtomar1130 Рік тому +1

    Sir kya yah har bar hota h ki agr base same rahte hai to power ko equality me compare kr sakte h?????
    Kyunki agr aisa hai to 1^1 =1^0 me 0=1 hojayega

    • @aritrasahaclass7roll15secb9
      @aritrasahaclass7roll15secb9 Рік тому

      Let's see
      Suppose a^n = a^m
      So a^(n-m) = 1
      Now take log of both sides,
      log a (n-m) = 0 ( log of 1 is 0)
      either
      n - m = 0
      n = m
      Or log a = 0
      a = 1
      Conclusion, for the no 1 and only for 1, m might not be equal to n.
      Hope ,it helps

    • @Bhuvan_MS
      @Bhuvan_MS Рік тому +1

      That rule is valid when base is not equal to 1.

  • @user-8uxj
    @user-8uxj Рік тому

    Best teacher ever sir!!
    I WOULD LIKE TO SUGGEST A SMALL THING 👉🏼👉🏼
    Sir ऐसी वीडियो बनाने से पहले इसे COMMUNITY टैब में पोस्ट कर दिया करिये लगभग 5-6 hours पहले 🙏🙏🙏

  • @shivnathbanerjee5868
    @shivnathbanerjee5868 Рік тому

    Sir aap x^4 se divide kar rahe hai both sides. Aisa ham tabhi kar sakte hai when x is not equal to 0. Aap ye chiz nahi bataye video me.
    So first we should check if x=0 is a solution of the equation or not.
    If x=0 is a solution then how can we solve this type of equation by this approach? Please tell me.

  • @jaishreeram3035
    @jaishreeram3035 Рік тому

    Sir ji x+2/x ki seedhe range se pta kr sakte hain ki soln hai ya nhi .Range by am gm (-2√2,2√2 ) me non real
    जय श्री राम

  • @pauselab5569
    @pauselab5569 Рік тому +1

    wait but this only works if you assume there are real solutions which doesn't always work and isn't general.

  • @prajnaparamitapatra9722
    @prajnaparamitapatra9722 10 місяців тому

    Very nice problem

  • @MultiGurmukh
    @MultiGurmukh Рік тому +1

    How did you know after changing octic equation into biquadratic, trail and error will give you a factor of it. Why didn't you try x values in the beginning only as all the coefficients of x were integers only.

    • @MathematicalPool
      @MathematicalPool Рік тому +2

      Isne question ko khud se set Kiya hai ki easily solve ho jaye nahi to mai challenge karta hu ki bas thoda sa change kar dunga aur solve karke dikha de .Mai challenge karta hu nahi kar payega.

    • @study-junction02
      @study-junction02 Місяць тому

      ​@MathematicalPool be respectful to sir

  • @bapilyrics1376
    @bapilyrics1376 Рік тому

    Sir yea to reciprocal equation

  • @dhruvbohra4424
    @dhruvbohra4424 Рік тому

    python produced 8 solutions of this equation {1, 2, -3/4 - sqrt(23)*I/4, -3/4 + sqrt(23)*I/4, 1/2 - sqrt(7)*I/2, 1/2 + sqrt(7)*I/2, 1 - I, 1 + I}

  • @ravisinha2165
    @ravisinha2165 Рік тому

    Olympiad ka batch hai to bataiye n sir 🙏🙏🙏🙏🙏

  • @ahmedbelkziz290
    @ahmedbelkziz290 Рік тому

    Thanks a lot

  • @mathematicssciencefun4525
    @mathematicssciencefun4525 Рік тому

    Sir please launch app for jee mains and advance 2024 for math please sir

  • @aksong0703
    @aksong0703 Рік тому +93

    Sir aap physics ka koi bhi topic khud se padhaiye naa 🙏🙏🙏

    • @mathmagic8577
      @mathmagic8577 Рік тому +11

      Sahi baat hai bhai uss field main bhi Ratna kam ho jayega aman sir ke ate hi

    • @divyanshdixit3445
      @divyanshdixit3445 Рік тому +9

      @@mathmagic8577 physics me ratna padh rha hai bro to bahut weak hai fir

    • @mathmagic8577
      @mathmagic8577 Рік тому +5

      @@divyanshdixit3445 achha,according to bohor L=nh/2×3.14 ye kaise proof kiyq gaya kuch padhate hai sidha bol dete hai Harare yaha agar tumhe samjme ata hai to bhaut badhiya baat agar nahi ata hai to tum bhi rat hi rahe bhai 😄 baki tum samjdar ho hi

    • @divyanshdixit3445
      @divyanshdixit3445 Рік тому +3

      @@mathmagic8577 bhai dekha jaye to ye chemistry ka hota hai par physics me bhi dediya hai aur chemistry ka to sabko pata hai ratna hi padta hai mai core physics ki baat kr raha hu like mechanics, waves ki baat kar rah hu agar usme ratna pad raha hai to weak hai aur ye jo hai vo bohr ne hypothesis kari thi to uska koi proof hi nhi hai to derive kaha se hoga

    • @mathmagic8577
      @mathmagic8577 Рік тому +1

      @@divyanshdixit3445 bhai yaha par Maine core physics nahi bola physics bola aur tumne bhi core physics nahi sirf physics ki baat kar rahe hai

  • @anshshukla9250
    @anshshukla9250 Рік тому +1

    Sir please bring jee advance toughest questions

  • @arjunajee638
    @arjunajee638 Рік тому

    Sir thank you for the great explanation,
    As you said to solve it yourself once, so i tried it , i got the one value of x that is (1)

  • @SANATAN_498
    @SANATAN_498 Рік тому

    Sir I have a doubt
    Sir linear equations me x ki 1 value aati hai
    Quadratic me 2 aate hai
    To octic me 8 values aane chahiye n ?
    🙏

    • @bhaveshsinghbisht
      @bhaveshsinghbisht Рік тому

      Yes ,
      8 values mai se 2 values hai jo REAL hai .
      Baaki 6 values COMPLEX NUMBERS mai ayegi .
      Sir ne nhi nikali hai , aap nikal sakte ho is formula se
      -b±√(b²-4ac)
      ______________
      2a

  • @shubhojithalder-xp8hd
    @shubhojithalder-xp8hd Рік тому

    Sir please differentiation class 11 PE ek series bana dijiye na. AAP ke channel me class 11 differentiation pe koi vi playlist nhi hai aur aap se parne ke baad aur kisi teacher ka lecture accha ni lagta hai

  • @avyakthaachar2.718
    @avyakthaachar2.718 Рік тому

    Amazing problem sir! Than you so much ❤👌👍

  • @gravitonX_
    @gravitonX_ Рік тому +4

    What if we apply contradiction method on √9 ?
    My answer is coming irrational but we all know that it is a rational number.
    Then what fundamental mistake is done while applying contradiction method on √9 ??

    • @vaibhavgupta8681
      @vaibhavgupta8681 Рік тому +3

      There is a theorem in which if p is a prime number and it divides a^2 i.e. p is a factor of a^2 , then p divides a also i.e. p is also a factor of a.
      When we proof √2 irrational , we get p as 2 which is a prime number and therefore we can apply this theorem and proof that √2 is irrational .
      But when we do this with √9 , we get a equation 9b^2=a^2
      Here , p is 9 BUT WE CAN NOT APPLY THE THEOREM BECAUSE 9 IS NOT A PRIME NUMBER.
      Since we can't apply this theorem, we cannot prove by contradiction that √9 is a irrational number.
      Therefore, √9 is a rational number as we all know.
      HENCE PROVED
      There is nothing wrong with maths, sometimes we just don't know how to apply rules.

  • @SorryItsAnEmergency
    @SorryItsAnEmergency Рік тому

    Sir app insanely nahi devta hai devta❤❤

  • @Prathamesh_Laddhad
    @Prathamesh_Laddhad Рік тому +1

    very very nice equation I loved this equation a lot

  • @mathimage4674
    @mathimage4674 Рік тому

    Love you sir❣️

  • @Questionpartice
    @Questionpartice Рік тому

    I saw every video .. That's done by u

  • @user-zh7he9bf3p
    @user-zh7he9bf3p Рік тому

    mene starting me x=1 put kia aur vo satisfy kia toh long division krke Quotient nikall lia first attempt me

  • @MangoLassiYT
    @MangoLassiYT Рік тому

    Sir why dont you start math olympiad series

  • @nikhilgone-ey3yf
    @nikhilgone-ey3yf Рік тому

    Sir please one shot videos banaiye for jee

  • @sonunayak9682
    @sonunayak9682 Рік тому

    Sir aise kitne equation hoti hai

  • @demonking8677
    @demonking8677 Рік тому +1

    Sir please teach us BSC SHM Chapter too, it's proof are kinda complicated, but if you teach it, then it will become so easy!!

  • @SachinPatel-mq5cs
    @SachinPatel-mq5cs Рік тому

    Live you sir you are legend

  • @AbhishekRaj-ho3ii
    @AbhishekRaj-ho3ii Рік тому

    Legend of mathematics

  • @Master_mind__235
    @Master_mind__235 Рік тому

    5:43 bhannat sir is dancing
    Machhli jal ki rani hai

  • @FazleAzimrupom
    @FazleAzimrupom Рік тому

    very nice.❤ I am from Bangladesh

  • @khandlamanhar9396
    @khandlamanhar9396 Рік тому +1

    Wow 👍👍 ❤️

  • @subhashdeshpande1772
    @subhashdeshpande1772 Рік тому

    Sur, you are freat !!

  • @sauravraj5271
    @sauravraj5271 Рік тому

    If it is asked how many total solution no matter real or imaginary what would be the answer??

  • @chemistryworld8986
    @chemistryworld8986 Рік тому

    Sir please make video on geometry new concept

  • @pandyapratham67
    @pandyapratham67 Рік тому

    Sir GOD OF MATHS 🥶👺

  • @studylikeheaven7962
    @studylikeheaven7962 Рік тому +1

    Sir jee mains pe 75 %criteria lag gaya hai sir

  • @abhijeetm29
    @abhijeetm29 7 місяців тому +1

    Ye kya tha 5:40 se 5:45 🤣🤣

  • @chinmayshetphayde2992
    @chinmayshetphayde2992 Рік тому +1

    Maine solve Kiya and 1 aya

  • @yashchaudhary9312
    @yashchaudhary9312 Рік тому

    sir phir se kbs show kijiye na

  • @svrat_O7
    @svrat_O7 Рік тому +2

    Me direct hit nad trial method

  • @aslprashant1152
    @aslprashant1152 Рік тому

    you are the gret

  • @hunterboy7689
    @hunterboy7689 Рік тому

    I LOVE YOU VERY MUCH SIR 💟 💟 💟 💟 💟 🤗🤗🤗🤗🤗🤗🤗🤗

  • @Mai_harshit07
    @Mai_harshit07 Рік тому +1

    Mene bhi same steps kiye the par beech me calculation mistake kar di🥺🙃

  • @Bgciesh
    @Bgciesh Рік тому

    Sir please make video on Taylor series

  • @swarnavabanerjee6908
    @swarnavabanerjee6908 Рік тому

    Sir, I have a little question 🙋‍♂️
    Why does this octic equation not follow the Descartes Sign Rule? According to that.. It must have 8 positive real roots... But, it only have 2 real positive roots!!
    If you kindly explain... I will be highly obliged🙏
    Please sir... Kindly keep my request 🥲

    • @priyanshshrivastava8842
      @priyanshshrivastava8842 Рік тому +1

      it is because the descartes rule states that the MAXIMUM no. of zeroes can be equal to the no. of sign changes, it does not say that the no. of zeroes has to be always equal to the maximum possible. the descartes rule says that maximum can be equal to no. of sign changes, so we have for this equation maximum as 8. but another possibility is 6, or 4 zeroes, or 2 zeroes.... or even 0 positive real zeroes. but we calculated it as 2, so we know answer is 2 positive real roots.

    • @syed3344
      @syed3344 Рік тому

      abey The degree of the equation= the number of roots
      Iske 6aur roots hai par woh complex roots hai toh unhe sir ne consider nhi kya

    • @swarnavabanerjee6908
      @swarnavabanerjee6908 Рік тому

      @@syed3344 Politely talking to you.. Kindly go through my comment once more.. Kindly understand what I meant to say & don't be oversmart🙂

    • @syed3344
      @syed3344 Рік тому

      @@swarnavabanerjee6908 lodu oversmart kon ho rha hai

    • @swarnavabanerjee6908
      @swarnavabanerjee6908 Рік тому

      @@syed3344 Typical psycho!! I think you should contact a psychologist 🙂 because you can't comprehend what I said

  • @chiragbulbule
    @chiragbulbule Рік тому +2

    Are these zeros coinciding? because ideally an octic equation should have 8 zeros right?

    • @saraswathygopal3322
      @saraswathygopal3322 Рік тому

      An octic equation must have eight zeroes but,they need not to be a real numbers as a solution
      In this octic equation,there are only two real solutions and the remaining six are unreal solutions

    • @chiragbulbule
      @chiragbulbule Рік тому

      @@saraswathygopal3322 so why would the graph look like?

    • @saraswathygopal3322
      @saraswathygopal3322 Рік тому +1

      @@chiragbulbule The graph will intersect only at 2 points on x-axis

  • @FutureWaitHim
    @FutureWaitHim Рік тому

    Sir ek inequality series layiye ❤

  • @study-junction02
    @study-junction02 Місяць тому

    8:40 mene yha tk solve karne k baad give up kr diya 😢

  • @vivekprajapati9560
    @vivekprajapati9560 Рік тому +2

    Yeah acha hai apne according problem banao phir use selfsolve karo😂😂😂😂😂😂😂😂😂😂

  • @sagarkunte5357
    @sagarkunte5357 Рік тому

    Super 👌

  • @vinayakmishra4702
    @vinayakmishra4702 Рік тому

    Namaskar guruji

  • @planeloverpilot4802
    @planeloverpilot4802 Рік тому +1

    bruh i struggle with cubic and hes doing octic😐

  • @Youplay123
    @Youplay123 Рік тому

    X=1 ek soln hoga iskaa

  • @Roshanbha260
    @Roshanbha260 3 місяці тому

    There is 8 solution for octoc equation

  • @ShreeHarivansh599
    @ShreeHarivansh599 Рік тому

    Ram ram ji 🙏

  • @Differentiate-x9h
    @Differentiate-x9h Рік тому +2

    Sir 60 mila hy mere ko math may is bar thik se par nehi paya tha 😞😞😭 keya may bsc math honours le sakta hu may math ko bohot pasand krta hu 😭😭

    • @aryanzark8201
      @aryanzark8201 Рік тому

      Pasand 😂karne se kuch nahi hota hai samay dena parta hai Jo tumse na ho payega lalla😂

    • @Differentiate-x9h
      @Differentiate-x9h Рік тому +1

      @@aryanzark8201 may de sakta hu samay . Apna 24 o ghante de sakta hu itna pagal hu or may math sirf marks k liye nehi parta. Janne k liye parta hu. Bus is bar kuch paresani se nehi ho paya tha lekin bar bar galti karne wala nehi may samjhe lalla

    • @aryanzark8201
      @aryanzark8201 Рік тому

      @@Differentiate-x9h bhai phir to ho jayega

  • @classxteaching..4067
    @classxteaching..4067 Рік тому

    Sir u r fire