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Hi,

How can I find the greatest value of $2k\sqrt{(r-k)(r+k))}$ with parameter $r$ such that $(r>k)$?

JMCF125
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Andi
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    What do you mean with "at great value expression"? – JMCF125 Jan 02 '14 at 23:46
  • not sure im bulgarian i used google translate – Andi Jan 02 '14 at 23:47
  • whats the biggest value that this expression can have depending on r where r> k – Andi Jan 02 '14 at 23:48
  • Ah, I see. I do not speak English nativly either. Check the Wikipedia page in Bulgarian, click to the English page, and see the name; that might help. – JMCF125 Jan 02 '14 at 23:49
  • i just what to know if: A = 2ksqrt((r-k)(r+k)) ; where r is parameter .what is the biggest value of A depending on k – Andi Jan 02 '14 at 23:50
  • I have suggested an edit for you. If you made any calculations or efforts to answer this you should put them in the question (click edit). Also check the FAQ and other help texts on the site clicking "help" above. You can Google-translate them to Bulgarian. – JMCF125 Jan 02 '14 at 23:54
  • no idea. Im making a program C++ where i need to slove this expression – Andi Jan 02 '14 at 23:57
  • This isn't a school excercise. Its hard for my knowadge – Andi Jan 02 '14 at 23:57
  • I believe it isn't a school exercise and that you can't do it yourself. But you have to try something. See other questions: the people who ask them don't know the answers, but they try to solve them basing on what they know. When they run out of ideas, they ask. Try putting several values for $r$ and $k$. What do you get? Show what you tried, even if it is wrong. – JMCF125 Jan 03 '14 at 00:01
  • can you tell me a theorem that would help me ? :/ – Andi Jan 03 '14 at 00:05
  • I can try tomorrow, it's over midnight where I live. But I'm sure someone will help you before that. – JMCF125 Jan 03 '14 at 00:08

1 Answers1

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Hint: Let us equivalently maximize the square of your expression. The square of your expression is equal to $$r^4-(r^2-2k^2)^2$$ (we "completed the square").

André Nicolas
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