Solve \(|x-3| + \sqrt{x^{2}-9} = 0\)

 Jun 28, 2020

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


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


We have to disbtrube the left side so


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

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

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