How do you find extraneous solutions when solving radical equations?

1 Answer
Jan 15, 2015

Let's start with an equation.

x-6=sqrtx

This can be solved easily by:

x^2-12x+36=x

x^2-13x+36=0

(x-9)(x-4)=0

x=9, x=4

but wait! we have to be careful whenever we square both sides of an equation.

Re-substitute the two answers into the original equation.

9-6=sqrt9
3=3

That's fine, one more.

4-6 = sqrt4
-2 != 2

Our extraneous answer is x=4

To find the extraneous answer of any equation, just find the solutions and then re-substitute the solutions into the original equation. The answer that results in an illogical equation is the extraneous answer.