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Loser66
 one year ago
Show that for all z on the circle z=3
\(\dfrac{1}{120}\leq \dfrac{1}{z^44z^2+3}\leq \dfrac{1}{48}\)
Please, help
Loser66
 one year ago
Show that for all z on the circle z=3 \(\dfrac{1}{120}\leq \dfrac{1}{z^44z^2+3}\leq \dfrac{1}{48}\) Please, help

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myininaya
 one year ago
Best ResponseYou've already chosen the best response.3I was thinking about using triangle inequality \[z^44z^23\le z^44z^2+3 \le z^4+4z^2+3 \\ 3^44(3)^23 \le z^44z^2+3 \le 3^4+4(3)+3\] then flipping things changes the direction of the inequality

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3I guess we could have done this instead on the that one side instead: \[a+b+c >ab+c>a \{bc\}=ab+c \\ \text{ instead of } \\ a+b+c>a+bc>abc\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3since the first way gives us what we want

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0The far left is 42, not 48 as we want.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3yep did you read my recent post

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Yes, I do. Thank you so much. ha!! I don't think it is that simple. hehehe ...

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0We have a similar problem in class and my prof gave us a very complicated explanation for that. I would like to know if there is any shortcut or not. That's why I post it here.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3but why don't you think my way works?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3I know you heard of the triangle inequality. That is what I used above.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3I'm confused when you said "I don't think it is that simple." did you mean to say "I didn't think it would be that simple."

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0@myininaya I didn't mean your method is wrong. I apology if I made you think that I don't believe your method. It is perfectly right. I got it.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3alright I just did misunderstood above

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0I know how to use triangle inequality. I just don't think of it on this problem.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Overestimate the problems is my "disease"

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3i think we all do that
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