Question

How do i check an equation for extraneous solutions?

Answer 1

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.

Answer 2

Example:


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

This suggests two solutions,
`x=0` and
`x=-1`.

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


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

which checks out, but


`√(-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` an extraneous solution, and the complete solution set (over the real numbers) is
`x=0`.