I think I got it. Can some one double check?

[Panama]

Solve

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




sqrt(2x - 1) = 1 + sqrt(x + 3)
2x - 1 = 1 + 2 sqrt(x + 3) + x + 3
x - 5 = 2 sqrt(x + 3)
x^2 - 10x + 25 = 4(x + 3)
x^2 - 10x + 25 = 4x + 12
x^2 - 14x + 13 = 0
(x - 1)(x - 13) = 0
x = 1 or x = 13

 

[Deleted member 4993]

Solve

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




sqrt(2x - 1) = 1 + sqrt(x + 3)
2x - 1 = 1 + 2 sqrt(x + 3) + x + 3
x - 5 = 2 sqrt(x + 3)
x^2 - 10x + 25 = 4(x + 3)
x^2 - 10x + 25 = 4x + 12
x^2 - 14x + 13 = 0
(x - 1)(x - 13) = 0
x = 1 or x = 13

You can check it yourself.

Put these values of 'x' in your original equation - and see if the equality is satisfied.

If the equality is satisfied - most probably you are correct.

If the equality is not satisfied - most probably you are incorrect or you got a superfluous (extreneous)solution due to "squaring".

Show us what do you get.

 

[fasteddie65]

What sometimes happens when you square both sides, is that you pick up an "extra" or extraneous root.
That's why you need to check your answers. Your algebra may not be incorrect; you just must be sure that both your answers check out correctly.