create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. use the equation below as a model:

Given

we have

Squaring both sides, we have

And finally

Note that, when we square both sides, we have to assume that

because we're assuming that this fraction equals a square root, which is positive.

So, if that fraction is positive you'll actually have roots: choose

and you'll have

Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose

and you'll have

Squaring both sides (and here's the mistake!!) you'd have

which is not a solution for the equation, if we plug it in we have

Which is clearly false

a

step-by-step explanation: