- #1

Dr. Mirrage

Ok, I know this question sounds incredibly elementary, but please don't just dismiss it, try to understand what I'm REALLY asking.

Ok, say we have [itex]x^{2} = 9[/itex]. I know the answer is [itex]x = \pm 3[/itex].

But I was just thinking about the general rule to this. I was thinking that what really happens is this first:

[itex]\pm x = \pm 3[/itex]

Which can then reduce to:

[itex]x = \pm 3[/itex]

so the general rule is that anytime you take something out of a square root, it gets a +/- sign.

Obviously no one would write it with a +/- in front of the x, it can be absorbed into the +/- on the other side. So please, don't say the step is "not needed" or "redundant" because I agree with you. I'm simply asking this because if it's not the case that there is a general rule like that, then we must come to the conclusion that there are certain "situations" in which you add it and sometimes you don't. I have been thinking about it, and I cannot see a situation in which writing the +/- on both sides is invalid. It always works, so why can't we say that this is what really goes on behind the scenes?

Sorry if this seems longer than it should be but I am in an argument with someone about this at the moment so I'm making my case.

For example:

say we know: x = 5

and we have this relation [itex]x^{2} = 25[/itex]

in this situation we have two solutions 5 works, and so does -5. Therefore [itex]\pm x[/itex] is a solution.

also keeping the +/- in front of x retains more information then just saying x alone, because if you know a solution to a problem is (+/-)x and you also know that x = 7, then you know right away that a second solution is -7.

So back to the beginning:

[itex]x^2 = 9[/itex] then the next step,

[itex]\sqrt{x^{2}} = \sqrt{9}[/itex]

now... am I to believe that there is a special rule that variables like x don't get the +/- ? Or, does it seem more general to just tack a +/- to both sides?

I apologize for what this must sound like, but I really would just like some closure on this, and I'm actually a little embarrassed to even have to ask such a question.

Ok, say we have [itex]x^{2} = 9[/itex]. I know the answer is [itex]x = \pm 3[/itex].

But I was just thinking about the general rule to this. I was thinking that what really happens is this first:

[itex]\pm x = \pm 3[/itex]

Which can then reduce to:

[itex]x = \pm 3[/itex]

so the general rule is that anytime you take something out of a square root, it gets a +/- sign.

Obviously no one would write it with a +/- in front of the x, it can be absorbed into the +/- on the other side. So please, don't say the step is "not needed" or "redundant" because I agree with you. I'm simply asking this because if it's not the case that there is a general rule like that, then we must come to the conclusion that there are certain "situations" in which you add it and sometimes you don't. I have been thinking about it, and I cannot see a situation in which writing the +/- on both sides is invalid. It always works, so why can't we say that this is what really goes on behind the scenes?

Sorry if this seems longer than it should be but I am in an argument with someone about this at the moment so I'm making my case.

For example:

say we know: x = 5

and we have this relation [itex]x^{2} = 25[/itex]

in this situation we have two solutions 5 works, and so does -5. Therefore [itex]\pm x[/itex] is a solution.

also keeping the +/- in front of x retains more information then just saying x alone, because if you know a solution to a problem is (+/-)x and you also know that x = 7, then you know right away that a second solution is -7.

So back to the beginning:

[itex]x^2 = 9[/itex] then the next step,

[itex]\sqrt{x^{2}} = \sqrt{9}[/itex]

now... am I to believe that there is a special rule that variables like x don't get the +/- ? Or, does it seem more general to just tack a +/- to both sides?

I apologize for what this must sound like, but I really would just like some closure on this, and I'm actually a little embarrassed to even have to ask such a question.

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