confused with the answer<> seems correct buttht's wrong wrong???????

question is

sqrt(x+1)-sqrt(x-1)=sqrt(4x-1) - - - - - - - - - - - - - - - - - - - - - - - (1)
squaring both sides
(x+1)+(x-1)-2*sqrt(x^{2}-1)=4x-1 - - - - - - - - - - - - - - - - (2)
solving and rearranging
1-2x=2*sqrt(x^{2}-1) - - - - - - - - - - - - - - - - - - - - - - - -(3)
once again squaring both sides;
1-4x= -4
x=5/4;
But it does not satisfy the first equation. it also doesn't satisfying equation number three, Is it reason for this????
If yes then why it is so?>?>?>?>?>?>(this is my question)

Re: confused with the answer<> seems correct buttht's wrong wrong???????

You seem to have started with an equation that doesn't have any real solutions. Let's consider a simpler problem: Find all real numbers x such that ##\sqrt x =-1##. If you square both sides, you get x=1. But x=1 doesn't satisfy the original equation, since ##\sqrt 1=1\neq -1##.

By squaring both sides, we only proved that if ##\sqrt x=-1##, then ##x=1##. This is an implication, not an equivalence, since x=1 doesn't imply ##\sqrt x=-1##. So we can't conclude that x=1. We can only conclude that there are no solutions with x≠1.