Answer
$a.\quad $not equivalent
$ b.\quad$ equivalent
$ c.\quad$ not equivalent
Work Step by Step
$a.$
These two are not equivalent, because $x^{2}=9 $ has 2 solutions ($\pm 3)$,
and the other has only one (x=3)
$b.$
Solution of $x=\sqrt{9 }$ is $x=3$
and is the only solution, because $\sqrt{a} $ is the positive square root of a.
The other equation has also only one solution, x=3.
These two are equivalent.
$c.$
Solving the first equation,
$x^{2}-3x+2=x^{2}+2x+1$
$-3x-2x=1-2$
$-x=-1$
$x=1$
there is only one solution.
Solving the second equation,
$x-x=-1+2$
$0=-1$
this one has no solutions.
These two are not equivalent
