Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

PlusMinus

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 confused

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: PlusMinus

why did you put a ± on the bottom one?

---

The Beginning Of All Things To End.
The End Of All Things To Come.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: PlusMinus

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)

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: PlusMinus

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)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: PlusMinus

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

is always -x, supposing they must be opposite, otherwise its ±x again

---

The Beginning Of All Things To End.
The End Of All Things To Come.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: PlusMinus

Thanks luca!

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: PlusMinus

Uh...just one more question, how can ±x + ±x = 0?

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: PlusMinus

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..."

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: PlusMinus

Ok, I just thought that ±x + ±x = 0 implied that either

x + x = 0 or -x -x = 0

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: PlusMinus

i was thinking about if the two pm's didnt have to have the same sign.

---

The Beginning Of All Things To End.
The End Of All Things To Come.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: PlusMinus

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..."