Find Solutions for |x-1|*|x+1|=0 with Step-by-Step Guide

[solar nebula]

Homework Statement

find all the numbers x for which |x-1|*|x+1|=0

Homework Equations

The Attempt at a Solution

|x-1|*|x+1|=0

|x-1|=0 or |x+1|=0

x-1=0 or x+1=0

x=1 or x=-1

but I think there's a flaw some in my attempt solution...or the whole thing is a flaw..
any help will be much appreciated!
Thanks!

 

[micromass]

It's completely correct!

 

[solar nebula]

It's completely correct!

But when I try to do the same thing for |x-1|*|x+2|=3 which is:

|x-1|*|x+2|=3

|x-1|=3 or |x+2|=3

x-1=3 or x+2=3

x=4 or x=1

But this solution does not make sense...
please help, Thanks!

 

[micromass]

Of course not. You basically did "xy=3 thus x=3 or y=3". This is obviously false.

To solve that, first do the following:

$$|x-1||x+1|=3$$

thus

$$|(x-1)(x+1)|=3$$

So the absolute value of the number (x-1)(x+1) equal 3. Then what can the number (x-1)(x+1) equal?

BTW I moved this to precalculus, because it obviously does not belong in calculus and beyond. Please post in the correct forum next time.

 

[DrewD]

In both cases you are following the procedure
$a*b=c \Rightarrow a=\frac{c}{b}$
which works as long as $b\neq0$. When you do it withe $c=0$ then $\frac{c}{b}=0$, but this is true for any $b$ (again, I'm assuming b is not zero). So you just skip right to $a=0$ or $b=0$.

micromass's explanation is probably more intuitive, but I like to think of things algorithmically.