Hii !
solve in the equation :
I agree with this up to the line and . This clearly implies the following line, but is not equivalent to it. In fact, appears to be a tautology, valid for all x. I certainly don't understand how it implies that .
Starting from and I would take the positive square root on both sides of those equations. The first one gives . For the second equation we need to be more careful. If x>0 then and we get . Thus the two equations together give , from which and therefore x=1.
But if x<0 then the positive square root of is , and a similar procedure to the previous paragraph gives , so that x=–1.
Thus there are two solutions, x = 1 and x = –1.