Question

Algebra Question!

Answer 1

So my teacher put up some solutions to some of my homework question.
The original equation was \[\frac{ 5 }{ \sqrt{x} - 2}=5\]
She used the quadratic equation and was able to get no solution for the equation. Here is the work she did.
http://prnt.sc/d1ia4i
http://prnt.sc/d1ia7l
However, I did a different way and I just cross multiplied to get that
\[\sqrt{x}-2=1\]
From here, I solved to get x is equal to 9.
Here is my work, sorry for the messiness.
http://prnt.sc/d1iaac
Even though we got different values for x, we both got no solution for the equation.
Is both ways technically correct?

Answer 2

\[\frac{ 5 }{ \sqrt{9}-2 }=5 \rightarrow \frac{5}{3-2}=5 ~\rightarrow 5=5\]
how did you get no solution ??
( the link isn't working on this laptop so i didn't check your work)

Answer 3

can you attach the file using the VV button below ?
sorry

Answer 4

Whoops, I wrote the equation wrong.
\[\frac{ 5 }{ \sqrt{x-2} }=5\]

Answer 5

I just took screenshots.

Answer 6

ahh okay

Answer 7

don't agree with the "teacher's" work
stopped with the first major error
using the distributive property with the denominator multiplying -2 by rt of x to get