There are two approaches for this question but ncert answer refers to the second one. What would be the appropriate method if it comes in board exams
You can follow whatever method that you wish to , unless and until you use some new concept/formula that’s not in NCERT you are pretty much good to go .
As far as algebraic manipulation is considered, you can go by any method that you wish to .
There’s nothing different that you’ll have to do for boards , the only difference is , you are not supposed to use the ‘shortcuts’ like L hospital for limits , etc . Else there isn’t any restriction that you need to follow a specific method only.
Best method put x+2=t^2 and then do it