This kind of thing commonly happens when you're exponentiating by an even power, btw. Say y=sqrt(5) identically, therefore y^2 = 5, but if you solve for y, you get y = +/- sqrt(5). Our squaring operation just injected a false root into the solution.

You do have to be careful when you determine that a root is extraneous.

For example, computing a negative length for the side of a triangle might be an extraneous root, or it might mean that the problem has no solution, or it might be an indication that we've set up the problem wrong - or it could be an indication that the problem space is a little more complicated than we had supposed.

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