Respuesta :

LammettHash
Example:

[tex]\sqrt x(x+1)=0[/tex]

This suggests two solutions, [tex]x=0[/tex] and [tex]x=-1[/tex].

However, upon plugging these solutions back into the equation, you get

[tex]\sqrt0(0+1)=0(1)=0[/tex]

which checks out, but

[tex]\sqrt{-1}(1-1)=0[/tex]

does not because [tex]\sqrt x[/tex] is defined only for [tex]x\ge0[/tex] (assuming you're looking for real solutions only). So, we call [tex]x=-1[/tex] an extraneous solution, and the complete solution set (over the real numbers) is [tex]x=0[/tex].
An extraneous solution is a solution that arises from the solving process that is not really a solution at all! Specifically, whenever you raise both sides of an equation to an even power, you must check for extraneous solutions.