- #1

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For extra information the crit points are (0,0,0) (-1,1,1) (1,-1,1) (1,1,-1) (-1,-1,-1)

Thanks!

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- Thread starter Typhon4ever
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- #1

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For extra information the crit points are (0,0,0) (-1,1,1) (1,-1,1) (1,1,-1) (-1,-1,-1)

Thanks!

- #2

Dick

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- #3

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What's the "algebraic" way of doing this? Multiple rounds of substitution?

- #4

Dick

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What's the "algebraic" way of doing this? Multiple rounds of substitution?

Yes, basically. If e.g. x+yz=0 then either y=(-x/z) or z=0, subsitute that into the other equations. Explain how you got your solutions.

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- #5

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Yes, basically. If e.g. x+yz=0 then either y=(-x/z) or z=0, subsitute that into the other equations. Explain how you got your solutions.

I just looked at this and thought of good numbers that would satisfy the equations. That's why I wanted a more systematic way of doing it. The substitution looks like a real headache to do.

- #6

Dick

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I just looked at this and thought of good numbers that would satisfy the equations. That's why I wanted a more systematic way of doing it. The substitution looks like a real headache to do.

OK, you just solved by inspection. Doing it systematically isn't that much of headache. Just do it. If I substitute y=(-x/z) into the second relation I get x(1-z^2)=0 after a little algebra. What does that tell you?

- #7

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Well I get that x=0 and z=+-1

If I plug into the third one I get x=+-z and z=+-x. Where should I start plugging things in next?

If I plug into the third one I get x=+-z and z=+-x. Where should I start plugging things in next?

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- #8

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OK, you just solved by inspection. Doing it systematically isn't that much of headache. Just do it. If I substitute y=(-x/z) into the second relation I get x(1-z^2)=0 after a little algebra. What does that tell you?

Well I get that x=0 and z=+-1

If I plug into the third one I get x=+-z and z=+-x. Where should I start plugging things in next?

- #9

Office_Shredder

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Well I get that x=0 and z=+-1

That's actually an or, not an and that you want

- #10

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That's actually an or, not an and that you want

Oh ok. Thank you. So now that I know x=0 or z=+-1 what should my next step be? Should I plug 1 and -1 into the first equation?

- #11

Dick

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Oh ok. Thank you. So now that I know x=0 or z=+-1 what should my next step be? Should I plug 1 and -1 into the first equation?

You know you are going to get 5 different solutions. Take those 'or' cases separately. In solving the first equation you had the z=0 OR x=(-y/z). First supposing z=0 what can you conclude about x and y? Then after solving the second equation consider the cases x=0, z=1 and z=(-1) separately. Substitute anywhere you like.

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