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 Post subject: AIME 1983 problemPosted: Fri, 1 Jul 2011 18:18:54 UTC
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Suppose that the sum of the squares of two complex numbers x and y is 7 and the sum of the cubes is 10. What is the largest real value that x + y can have?
[/tex]

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 Post subject: Re: AIME 1983 problemPosted: Fri, 1 Jul 2011 18:49:56 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 7622
Location: NCTS/TPE, Taiwan
mun wrote:
Suppose that the sum of the squares of two complex numbers x and y is 7 and the sum of the cubes is 10. What is the largest real value that x + y can have?

There are 6 points of intersection of the plane quadratic and the plane cubic , and it is not that difficult to find what they are:

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 Post subject: Posted: Fri, 1 Jul 2011 22:07:05 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX
This belongs in Miscellaneous. Topic moved.

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 Post subject: Re: AIME 1983 problemPosted: Sat, 2 Jul 2011 13:38:27 UTC
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Joined: Mon, 19 May 2003 19:55:19 UTC
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Location: Lexington, MA
Hello, mun!

I think I've solved it . . .

Quote:
Suppose that the sum of the squares of two complex numbers and is 7,
and the sum of the cubes is 10. .What is the largest real value that can have?

.[1]

Square [1]:
. .
. . .[2]

Cube [1]:
. .

. .

. .

. .

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