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mathmath333
 one year ago
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mathmath333
 one year ago
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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align}& \{p,q,r\}\geq 0\hspace{.33em}\\~\\ & p+q+r=10 \hspace{.33em}\\~\\ & \normalsize \text{find the maximum value of} \ (pq+qr+pr+pqr)\hspace{.33em}\\~\\ \end{align}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because it 4 p's, 3 r's and 2 q's and you can only make two sets of (p=q=r)=10

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if im doin it right lol

freckles
 one year ago
Best ResponseYou've already chosen the best response.2So p,q,r are real numbers?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2We know 70 something can be achieved since \[\text{ if } p=q=r=\frac{10}{3} \\ \text{ then } 3 (\frac{10}{3})^2+(\frac{10}{3})^3=70.37\] but there might be a higher number we can reach then that maybe thinking...

freckles
 one year ago
Best ResponseYou've already chosen the best response.2that should be an approximation symbol there

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} & a.)\ \geq 40\ \cap \leq 50 \hspace{.33em}\\~\\ & b.)\ \geq 50\ \cap \leq 60 \hspace{.33em}\\~\\ & c.)\ \geq 60\ \cap \leq 70 \hspace{.33em}\\~\\ & a.)\ \geq 70\ \cap \leq 80 \hspace{.33em}\\~\\ \end{align}}\)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2well if there is a bigger number than 70.37 and you have no other inequalities then process of elimination would mean...

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0the correct option given by book is option \(c.)\) the book also gave a hint to assume \(p=4,q=3,r=3\)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2that is assuming p,q,r are integers but that was never given

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0oh sry i forget they are integers given.

freckles
 one year ago
Best ResponseYou've already chosen the best response.2oh I would use the book's hint then :p

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0but book's solution is kind of trial and error

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I think those numbers came from being close to 10/3

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0or is thaat the only way in case they are integers

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3yeah but this symmetry stuff doesn't work always, remember we saw it failing multiple times before

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0in case other question comes with restriction given as integers, should i use the same method as described by the book

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3that method has no mathematical justification, simply saying "by symmetry" wont do

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you either need to use AMGM inequality or other standard methods

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0using AMGM even in case of integers ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3it works on reals but you can use it to pick the closest integers
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