Stephanie is student teaching at her local high school. She has to help her instructor write a test. She has to write a radical equation where the solution is extraneous. She also has to write a radical equation where the solution is non-extraneous. Help Stephanie write one radical equation where the solution is extraneous and another equation where the solution is non-extraneous. Using complete sentences, explain each step when solving to justify your examples.

Question

anonymous · Answer

@satellite73 @Loser66 @Compassionate

anonymous · Answer

@hilbertboy96

anonymous · Answer

and example of an extraneous radical equation is where one of the answers solved for it can not be included. One example of this is

$$x-6 = \sqrt{x}$$

because when you solve for x you get
$$x^2 - 12x + 36 = x$$
$$x^2 - 13x + 36 = 0$$
$$(x-9)(x-4) = 0$$
$$x = 9, x = 4$$

How ever only 9 (meaning it is non-extraneous) works in the original and 4 does not (you can try to verify)


Non-extraneous just means all solutions work in the equation. One example could be
$$\sqrt{x-4} = 2 $$ 
$$x - 4 = 4$$
$$x = 8$$

8 is non-extraneous because if works in the original equation

anonymous · Answer

As for wording the explanation in complete sentences that is up to you but that is the basic concept.