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Topic: Sum of fourth powers (Read 396 times) |
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NickH
Senior Riddler
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Sum of fourth powers
« on: Mar 5th, 2004, 12:35pm » |
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If the sum of three numbers is 6, the sum of their squares is 8, and the sum of their cubes is 5, what is the sum of their fourth powers?
[edit]Changed the numbers from (1,15,3) to (6,8,5) to give a more interesting answer.[/edit]
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| « Last Edit: Mar 6th, 2004, 2:54pm by NickH » |
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Barukh
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Re: Sum of fourth powers
« Reply #1 on: Mar 7th, 2004, 1:28am » |
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[smiley=blacksquare.gif]
The answer I've got is 0. I used ideas from the Symmetric Expressions thread.
[smiley=blacksquare.gif]
Nice riddle, Nick! Are you sure it belongs to easy section?
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NickH
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Re: Sum of fourth powers
« Reply #2 on: Mar 7th, 2004, 5:26am » |
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That's the answer I got.
Based on your comment, I'm not sure whether I used the same method. There is a solution that doesn't require a3 + b3 + c3 and a4 + b4 + c4 to be expressed in terms of elementary symmetric expressions. But you may be right; I probably should have placed this puzzle in the medium section!
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