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How do i check an equation for extraneous solutions?

User Hoha
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2 Answers

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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.
User FirasKoubaa
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6 votes
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.
User Enze Chi
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8.5k points

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