Solving a problem by four different methods

[@BHANNATMATHS]

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[@MdsamimAlam-s7m]

SIR PLEASE REPLY THIS METHOD IS IT CORRECT OR NOT .. Method 5 this my own solution a²+b²=4 ......eq 1 c²+d²=9 .......eq 2 Multiply eq 1 and 2 We get (ac)²+(ad)² +(bc)²+(bd)² =36.......eq 3 When rearrange eq3 Like this ..... (ac)²+(bd)²+ (ad)² +(bc)²=36 eqn 4 Then we can replace (ac)²+(bd)² by (ac+bd)²-2acbd in eqn 4 We get (ac+bd)²-2acbd +(bc)²+(ad)²=36 For (ac+bd)² maximum the. Term - 2acbd +(bc)²+(ad)² must be zero There the(ac+bd)²=36 Answer is 6

[@Love_seeker-143]

Sir aap koi advanced calculus ki book bata do pls jisme solutions na ho

[@Love_seeker-143]

Pls pls

[@4dityap]

𝗧𝗜𝗠𝗘𝗦𝗧𝗔𝗠𝗣𝗦 🕰️ 1:37 - TRIGONOMETRY 3:37 - VECTORS 4:53 - COMPLEX NUMBERS 7:36 - DETERMINANTS

[@starkxlavanya30]

method 5)am gm method6)cauchy swartz inequality 7)most amazing one using ptolemey therom 2,3 be length of diagno se d1*d2=ac+bd

[@starkxlavanya30]

7th method koi nhi btaega 😁 mere alawa

[@sleha4106]

​@@starkxlavanya30batade bhai

[@CatalpaGG]

5th seh kese kroge

[@Jai_mata_di_jai_radhe_krishna_]

Op bro I agree I got the solution by these methods also these are more efficient

[@sirak_s_nt]

@@starkxlavanya30 I guess ptolmy lagane ke liye a, b, c, d will have to represent sides of a cyclic quad for which a, b, c, d need to be positive which is not given in the question. Same shortcoming in case of AM-GM. C-S is accepted.

[@AnmolSingh-ts8id]

method 6 may be - when we need to maximize ac+bd so therefore we can equate terms of a^2+b^2 = 4 and c^2+d^2= 9 hence a^2 = 2 and c^2= 9/2 on multiplying and taking root of (ac)^2 we get 3 similarily bd= 3 so answer comes out to be 6

[@harshwardhansathe8071]

Daym😂 man you are a mathematical genius ❤❤

[@shauryagiri4867]

Sir we can do this question by one extra method also which is cauchy-schwarz inequality which we have learned in sequence and series

[@question9963]

That's not an extra method Cauchy-schwarz inequality derivation comes from vector method

[@vivekbanerjee1939]

We can do this by using Cauchy- Schwarz inequality too.😊

[@udayanchaki5620]

But using it would give you max value as 36

[@udayanchaki5620]

And also cauchy is used when there is one set of square of variables and other set of squares of constants and some linear expression between consecutive variable and constant is brought forward . So how do you cauchy?

[@Therookie184]

what about rearrangement inequality?

[@sirak_s_nt]

​​@@udayanchaki5620you need to revise cauchy

[@solunke.pranav]

Well it also comes from vector scalar product

[@aashishgupta2207]

We can also solve this by "Cauchy Schwarz Inequality"......

[@lakshya__gupta]

In. Which class is this??

[@champu823]

@@lakshya__gupta 11th

[@lakshya__gupta]

@@champu823 chapter??

[@champu823]

@@lakshya__gupta there is no chapter it depends on your teacher if he teaches you that

[@Rahul-br9sz]

Its pretty much the same as vectors method though

[@iit_jee-2024]

Method 5 : Sir maine coordinate geo ka istemal kiya Dono eqn ko circle ke form megraph banya the waha se max value pe comment kar diya

[@sambitray2242]

Excellent explanation sir

[@Sd4ss]

Sir kabhi Aisa socha nahi tha🤯

[@azqureshi9668]

sir (ad-bc)^2 ki min. Value 0 kese kari 7:03

[@phatdawg6935]

dono taraf square krke (ac+bd)^2 ko subject bana

[@azaz-ct9jm]

Sir, ioqm ki tayari karao please.

[@chsrinivasrao4753]

Sir metrics method par bhi ik detail video banao sir please🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏

[@arnavmeena525]

Sir first method me a=3sinx rakhne par -3 ≤a≤3 condition impose ho gayi jo question ko thoda contradict kar rhi hai where a, b, c, d are any real numbers hai.

[@rakshitmodi3045]

Actually real number bola hai par a^2+b^2 =4 means agar a max karna hai tuh b minimum bhi kar de tuh a 2 se zyada nhi hoon sakta so ye valid hai

[@RaniDevi-xt4hq]

a agar 2 se bada ya -2 se chota ho gya b complex ho jayega

[@akashshingare6374]

We can also solve it by ptolemy theorem

[@shauryagiri4867]

ha tu toh ise pythagoras se bhi solve kar dega bhai

[@shinokaminamikaze]

Sir please solve this question using calculus

[@anujkumar035]

Waah❤

[@chsrinivasrao4753]

Vector method par ik detail video banao sir please🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏

[@Omprakash-sg3my]

Sir ap Olympiad ke liye padhaeaaa

[@Sahil.YouTube.]

Sir also solve this problem by Matrix and Geometry

[@KanvRajput]

Sir IOQM KI CLASSES

[@Sunilverma-xu5hz]

Sir .. soch ko door Tak kese bheje..

[@Allenite_RajModi]

Revision checklist jaldi Lao sirji

[@sudhakarwajirgave5838]

Couchy swarts ineq

[@Abcdefghi123-d8i]

Sir can we use the concept of AM and GM, I used it and I am also getting max value =6 , so there are total 5 solutions for this question.

[@manishkumarmeena2553]

Good bro i know you are getting correct answer thats good, but if we actually see the question a,b,c,d belongs to real number and am gm is only for positive number.. so you are getting answer is good but can't say it's really solution

[@bred3620]

​@@manishkumarmeena2553use am GM on a^2 not a

[@FamilyVibesYT]

Find the values of x, y , z and A in given equation x²+y² +z²=2A where x=y-1, y = z-1 and z=x-1 and x+y+z=1.50 sir plss solve this

[@Therookie184]

sir why cant we use rearrangement inequality in this problem ?? using that my answer is coming 13/2

[@Rahul-br9sz]

I am not really sure how you solved it but its probably some mistake in forming inequalities since it isnt given that all the entries in the question are positive Btw this is a two liner problem using cauchy schwarz inequality although its pretty much same as the vector method

[@sirak_s_nt]

Direct question of Cauchy inequality

[@divyakumar8147]

thanks sir

[@EmanuelBenedict-cr2xi]

🙏

[@rambhagorain5009]

Sir ISI ke questions karao

[@shashanktiwari6533]

Wow sir ❤❤❤

[@goldeneditor4872]

Method 5- By AM GM a²+b²= 2ab a=2/b and C=9/2d ac=9/bd by AM GM (9/bd +bd)/2= √9 max value = 6

[@factzblowing2732]

Very good solution 👍🏻😮 Best solution

[@goldeneditor4872]

👍👍

[@sirak_s_nt]

bd is not necessarily positive

[@goldeneditor4872]

​@@sirak_s_nt max value is 6

[@champu823]

Not a valid solution since a,b,c,d are not necessarily positive real numbers They can be negative also And AM -GM only works for positive numbers

[@4Das369]

Maja a Gaya sir ❤

[@Karan-1888]

Method 6 Using Number Theory

[@sirak_s_nt]

How?

[@aadijaintkg]

Another method AM - GM

[@Pscydi]

Pythagoras theorem?

[@BETATRON-LightUpYourlife840]

Hello sir mera apko pranaam 🙏🙏🙏🙏🙏🙏

[@atmaramsharma6906]

2

[@BharatPratap197]

Sir I want to become just like you in maths and personality but my personality not bad 😅

[@itsbikidey]

Think wider.

[@skgammer9566]

lim x →∞ { e/ ( 1 + 1/x )^x }^x please solve this ❤

[@AshuuuiiAshhu]

Is it -infinity

[@TechToppers]

For all people screaming Cauchy Schwarz, vector method Cauchy ka proof hi hota hai!

[@champu823]

I solved by using cauchy's inequality (a² +b²)(c² +d²) ≥ (ac+bd)² ac +bd ≤6 (ac +bd )max = 6

[@mehulkala8922]

Bro caushy's inequality is also derived from vectors

[@champu823]

@@mehulkala8922 didn't knew it can also be proved using vectors I only saw prove based on algebra Which goes like this (a1 +xb1)² +(a2 +xb2)² +....+(an +xbn)² ≥0 Now if we open the brackets Collect We get a quadratic in x (b1² +b2²+..+bn²)x² +2(a1b1 +a2b2 +..+anbn)x +(a1² +a2² +...+an²) ≥0 Now for this to be true for all value of values of x D≤0 Hence ,we get (a1² +a2² +...+an²)(b1² +b2² +..+bn²) ≥(a1b1 +a2b2 +...anbn)²

[@mehulkala8922]

​@iamgoodperson484bhai bas kull Mila kar main baat hai caushy's inequality yaad karlo (a^2+b^2+c^2)(d^2+e^2+f^2)≥(ad+be+cf)^2 hota hai and ye two vectors ke dot product se derive hota hai.

[@saurabhvishwa1916]

NTA be like:- mere ko yesa Question ab Dena hi nhi 😅

[@MdsamimAlam-s7m]

Method 5 this my own solution a²+b²=4 ......eq 1 c²+d²=9 .......eq 2 Multiply eq 1 and 2 We get (ac)²+(ad)² +(bc)²+(bd)² =36.......eq 3 When rearrange eq3 Like this ..... (ac)²+(bd)²+ (ad)² +(bc)²=36 eqn 4 Then we can replace (ac)²+(bd)² by (ac+bd)²-2acbd in eqn 4 We get (ac+bd)²-2acbd +(bc)²+(ad)²=36 For (ac+bd)² maximum the. Term - 2acbd +(bc)²+(ad)² must be zero There the(ac+bd)²=36 Answer is 6

[@elipsedhiman7886]

No as 1 is negative quantity and 2 are positive quantity if all of them were negative then ur logic would have been correct

[@MdsamimAlam-s7m]

@@elipsedhiman7886 - 2acbd +(bc)²+(ad)² if we solve this quantity we will get (bc -ad)² you can see the last step of sir solution by determinant method .... (bc -ad)² the positive quantity must be zero

[@MdsamimAlam-s7m]

@@elipsedhiman7886

[@elipsedhiman7886]

@@MdsamimAlam-s7m Maine kab kaha sir ne sahi kiya

[@elipsedhiman7886]

@@MdsamimAlam-s7m and hn exam me pls do all this 👍

[@mohdanas5688]

ligands will understand .. sir gave a mini studio tour 😂😂😂😂😂😂😂😂

[@sleha4106]

Ligand toh Bhai sirf tu hi h

[@clarxz1141]

Hi sirrr

[@Kanishk92921]

1st comment❤

[@Kanishk92921]

1st❤

[@learnwithdk5533]

Pata nahi mera comment kab viral hoga

[@asheeshkumar8517]

Padh le beta

[@subhadipiitian3451]

Sir i am bsc mathematics student now I am preparing for iit jam and my preparation... Is running good

[@Skp.killer688]

Sir p&c par koi oneshot aasan lecture bana do 🙏🙏🙏🙏