Solving Radical Equations

Question

Question. (rootx+1) - (root x-2) =1

how to solve this problem step by step.

and I don't know exactly how to answer is x=3

Answer 1

sqr(x+1) -sqr(x-2) = 1

x=3

sqr(3+1) -sqr(3-2)

=sqr4 - sqr1

= 2-1

= 1

square both sides

x+1 - 2sqr(x^2 -x-2) + x-2 = 1

sqr(x^2-x-2) = x-1

square both sides again

x^2-x-2 = x^2-2x+1

2x-x=1+2

x=3