+0  
 
0
92
2
avatar

Solve \(|x-3| + \sqrt{x^{2}-9} = 0\)

 Jun 28, 2020
 #1
avatar
0

Hi there! I have figured out the answer but dont really know how to put it into words... 

lets try though!

So we know that \(|x-3|\) will have to be positive because of the absolute value. 

and if we expand out the radical \(\sqrt{x^2-9}\) we get\(\sqrt{(x-3)(x+3)}\)

Now that we have this we can subtract \(|x-3| \) from the left side. This means that our new equation is

\(\sqrt{(x-3)(x+3)}=-|x-3|\)

note: because of the absloute value we can get rid of the negitive

Because there is a radical we can square both sides to get

\((x-3)(x+3)=|x-3|^2\)

We have to disbtrube the left side so

\(x^2+3^2=(x-3)^2\)

simpify \(3^2=9\) you can solve from there!

also this might not be the best way to solve a question like this because it is my personal way aswell the way I learned it.

Hope this helps

~Wolf :D

 Jun 28, 2020
 #2
avatar+27660 
+1

Hmmmm..... I am not sure this is possible....

  sqr (x^2-9)  will always be positive     which would mean  |x-3| must be NEGATIVE for the terms to ADD to 0......absolute values cannot be negative.....  Did you enter your question correctly?

 Jun 28, 2020

43 Online Users