Before squaring both sides and solve for x, you must put the condition that the right-hand member is nonnegative.
.
So, the other two roots, are not in this interval.
Another way to solve the equation:
Let .
Then
But .
The problem is solve for x:
If I do this in the 'normal' way, by isolating the square root and squaring both sides, I get:
This yields
Why did the two extraneous roots appear?
Thanks!
(I realised you can immediately set , but that's not the point)