SOLUTION: can you please solve over the reals, the sqrt 2x-1 minus the sqrt x-1 = 1

Question 21563: can you please solve over the reals, the sqrt 2x-1 minus the sqrt x-1 = 1
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
sqrt (2x-1) = 1+sqrt(x-1)
Square both sides to get:
2x-1 = 1+2sqrt(x-1) + (x-1)
Simplify to get:
2sqrt(x-1)= x-1
Square both sides to get:
4(x-1) = x^2-2x+1
x^2-6x+5=0
(x-5)(x-1)=0
x = 5 or x=1
Check both answers in the original equation:
If x=5 you get sqrt(9) 1+sqrt(4)
So, x=5 is a good answer.
If x=1 you get sqrt1=1+sqrt0
So x=1 is a good answer.
Cheers,
stan H.

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