Question

solutions to:

sqrt(3x)-sqrt(x+1)=sqrt(x-2)

Answer 1

i can get the solution x=-1 but there is supposed to be an x=3 solution too, but i can't figure out how to get it

Answer 2

{sqrt(3x)-sqrt(x+1)}^2={sqrt(x-2)}^2 (squaring both sides)
3x+x+1-2(sqrt(3x.(x+1))=x-2
4x+1-2(sqrt(3x.(x+1))=x-2
3x+3=2(sqrt(3x.(x+1))
(3x+3)^2=[2(sqrt(3x.(x+1))]^2 (squaring both sides)
9x^2+9+18x=12x^2+12x
12x^2-9x^2+12x-18x-9=0
3x^2-6x-9=0
x^2-2x-3=0
x^2-(3-1)x-3=0
x^2-3x+1x-3=0
x(x-3)+1(x-3)=0
(x-3)(x+1)=0
x=3 or x=-1

Answer 3

thank you good sir. i appreciate the help. :)