Mathematics: How do i check an equation for extraneous solutions?

How do i check an equation for extraneous solutions?

Ответ:

KylieAnne

17.01.2022

Mathematics

Example:

$\sqrt x(x+1)=0$

This suggests two solutions, x=0

and

.

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

$\sqrt0(0+1)=0(1)=0$

which checks out, but

$\sqrt{-1}(1-1)=0$

does not because $\sqrt x$ is defined only for $x\ge0$ (assuming you're looking for real solutions only). So, we call x=-1