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Maximum Value (Posted on 2002-06-19) Difficulty: 3 of 5
We have :
      x^2+xy+y^2=3 and
      y^2+yz+z^2=16
      A=xy+yz+zx
Find the maximum value of A. Find x, y and z when A=max value.

(Remember the category)

See The Solution Submitted by vohonam    
Rating: 3.2857 (7 votes)

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Some Thoughts re: Most of a solution - Solution confimed. | Comment 15 of 18 |
(In reply to Most of a solution by Brian Smith)

There are two maximum points on A. They are given by y=4/sqrt 31 and y=-4/sqrt 31. These are the only maxima on the curve A.
x=7/sqrt 31 y=4/sqrt 31 z=20/sqrt 31 A=8
x=-7/sqrt 31 y=-4/sqrt 31 z=-20/sqrt 31 A=8
This has been confirmed by solving dA/dy for all cases.
  Posted by Brian Smith on 2003-04-28 04:13:15

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