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September 6th, 2018, 01:55 PM   #1
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Solve this system of equations

x^2+yz+y^2*x=0
y^2+xz+z^2*y=0
z^2+xy+x^2*z=0
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September 6th, 2018, 03:45 PM   #2
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Ok. Done.
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September 6th, 2018, 03:54 PM   #3
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Hmmmm....a=0, b=0, c=0
Ahem!!
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September 6th, 2018, 04:15 PM   #4
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there is another real solution as well
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September 6th, 2018, 04:18 PM   #5
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Quote:
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there is another real solution as well
Tiger shot minus 2 in opening round?
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September 6th, 2018, 07:11 PM   #6
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Quote:
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Tiger shot minus 2 in opening round?
indeed he did
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September 6th, 2018, 08:42 PM   #7
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Thank you guys, though I guess, I didn't make myself clear enough. I meant: determine all real solutions and, having done so, prove that there are no other real solutions.

Last edited by Jungle12; September 6th, 2018 at 09:03 PM.
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September 7th, 2018, 03:54 AM   #8
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This is how you find them:

https://en.wikipedia.org/wiki/Newton%27s_method

This is how you prove there aren't any others:

6.4.2 Cylindrical Algebraic Decomposition
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September 7th, 2018, 03:59 AM   #9
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Quote:
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I didn't make myself clear enough.
Where did you get this problem from?
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September 7th, 2018, 06:34 AM   #10
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A mate of mine asked me to solve it for them, I wasn't able to, so I asked for it here
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