Problem: Find Minimum value of PA+PB+PC , which have constrained that a+b+c is constant integer (for Simplicity let it be ' 5 ' )

I want only geometric approach . This is open discussion , if you are able to get some steps then share it with us , we all brilliantian's together try to complete that.

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## Comments

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TopNewestGuys, I think there is a very simple way to solve this problem.... I have that feeling, check out my solution to see if it is right here

@Deepanshu Gupta @Mvs Saketh

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I have posted a geometry based solution here.

And thanks for starting this discussion, because I hadn't seen this question. :)

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Hey I have one doubt , If I treat this side as Force Vector's and Try to minimize the restultant force then what will we get ? What Do you Think about it ? May be this not fit in this situation , do we make a suitable situation for using this concept ? I'am really Interested in making an situation in which we can analyse Such Minimum value of expresion using Force concept. I'am not able to come up with particular conclusion about such situation individually . Could You Please Help me out . This may sound silly Bit , but it will be great if we do some discusion on it @Shashwat Shukla and all other guy's what do you think ? @Mvs Saketh what do you think ?

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The truth is @Deepanshu Gupta , that is almost exactly the solution, that is the solution Raghav posted, however it need not be force, it can be any vectors, infact the same inequatlity u used to solve the "is it too complex" is more or less applied here,

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link . It contains info on roughly all the topics in Maths . But you'll have to search for it !! Check it out !!

Here's theLog in to reply

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this

trypage 105 and 106

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But I haven't seen such a problem on brilliant... Which one are you talking about?

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This is that problem regarding inequalities right , i too was thinking in the exact manner , how to minimise PA + PB + PC,

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Yes , I still haven't tried it yet but will Lagrange Multipliers do the job ?

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Yes it does.

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\( (a\theta+b\lambda+c\delta) \le \sqrt {(a^2+b^2+c^2)(\theta^2+\delta^2+\lambda^2)}\)

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for any two vectors

\(\vec { a } .\vec { b } =\quad \left| \vec { a } \right| \left| \vec { b } \right| cos\theta \quad \le \quad \left| \vec { a } \right| \left| \vec { b } \right| \\ \\ ({ a }_{ 1 }{ b }_{ 1 }+{ a }_{ 2 }{ b }_{ 2 }+{ a }_{ 3 }{ b }_{ 3 })\quad \le \quad \sqrt { { a }_{ 1 }^{ 2 }+{ a }_{ 2 }^{ 2 }+{ a }_{ 3 }^{ 2 } } \sqrt { { b }_{ 1 }^{ 2 }+{ b }_{ 2 }^{ 2 }+{ b }_{ 3 }^{ 2 } } \)

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I dont get notifications!

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here is the note .

Check your email id or wherever you registered on Brilliant from . BtwLog in to reply

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Thanks all Guy's , Sorry for late reply , actually My BSNL Broadband Internet become dad Last Night , I really get offended from this broadband connection. But Any way Thanks For this discussion and sharing Your Ideas related to that question .

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Hey thanks guy's and sorry , I got too many interesting stuff's so I'am going on my study table since I'am too excited and wanted to analyse them. I will report you back after doing some work on them , till than thanks alot for help. Good Night Brothers !

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goodnight bro!

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