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I'm a bit confused about the +- sign.
If
Then
Do the +-'s cancel out or what???
If you have this, then multiply
to both sides, where does the +- go? Does it stay with the or go to the other side?? yea im a bit confusedOffline
why did you put a ± on the bottom one?
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Also, +-'s are a major headache when it comes to the distributive law! How is it supposed to work?
...What happens if you multiply
by ... or by ?Also... is
????Last edited by Identity (2007-06-29 21:40:51)
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Because by looking at the first equation, you know that you will square root both the top p and the bottom q. Can't this be directly written also as
? Because you have the choice to sqrt them separately?Last edited by Identity (2007-06-29 21:43:47)
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think of ± as a normal algebraic variable:
±x + ±x has 3 potential values, -2x, 0 or 2x
(±x)(±x) is x, supposing ±'s most always be the same, otherwise its ±x
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Thanks luca!
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Uh...just one more question, how can ±x + ±x = 0?
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If you are ever in doubt of what to do with a ±, write it out as separate equations and solve them individually. If you have n ± in an equation, you will get 2^n different equations.
So let me go through your example:
±x + ±x = 0
This is saying:
x + x = 0
x - x = 0
-x + x = 0
-x - x = 0
Solving the first equation, we get 2x = 0, so it must be that x = 0. x - x = 0, so x can be any number. -x + x = 0, so again, any number. -2x = 0, so x = 0.
So there are "four" different solutions to the above equations: x = 0, x = anything, x = anything, x = 0. We would normally call this two solutions with two repeated roots.
If this sounds confusing, just think about solving a quadratic equation. It's the same thing, you get 2 roots.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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Ok, I just thought that ±x + ±x = 0 implied that either
x + x = 0 or -x -x = 0
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i was thinking about if the two pm's didnt have to have the same sign.
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I've never seen such interpretation of it, luca. The way I figured it:
x ± 2 means x + 2 or x - 2
So ±x ± x means ±x + x or ±x - x. In turn, each of those mean (x + x or -x + x) or (x - x or -x - x).
No?
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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