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The Value of ABS[?]

Date: 08/24/2010 at 22:18:19
From: Jen
Subject: When you use absolute value in finding roots?

In class sometimes when the teacher is at the board doing problems with
roots and lots of variables, all of a sudden an absolute value symbol will
appear in the answer.

When exactly does this pair of vertical lines come into play?

Date: 08/25/2010 at 10:11:27
From: Doctor Ian
Subject: Re: When you use absolute value in finding roots?

Hi Jen,

Suppose I know that the value of some variable, if squared, is equal 
to 4:

   x^2 = 4

There are TWO solutions to this equation -- one positive, and one 

   x^2 = 4

     x = 2 or -2

The absolute value symbol is a way of specifying both of those values 
at once:

   x^2 = 4

     x = 2 or -2

   |x| = 2            This means the same thing as 
                      the previous line.   

It's just a convenience, so you don't have to keep writing subsequent
equations twice (once for the positive value, and again for the negative

Does it make more sense now?

- Doctor Ian, The Math Forum 
Associated Topics:
High School Basic Algebra
High School Square & Cube Roots

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