- #1

DS2C

## Homework Statement

Looking for an explanation as to why, when we square both sides of an equation, we can get extraneous solutions. That is, why can we square both sides of an equation, and sometimes the solutions we get are not true.

In my book, it gets a little wordy and doesn't make a lot of sense. It says that "If both sides of an equation are raised to the same power, all solutions of the original equation are among the solutions of the new equation. This does not say that raising both sides of an equation to a power yields an equivalent solution."

This makes no sense.

## Homework Equations

An example:

$$\sqrt {4 - x} = x - 2$$

$$\left(\sqrt{4 - x}\right)^2 = \left(x - 2\right)^2$$

$$x = 0 ~or~ x = 3$$

## The Attempt at a Solution

0 Results in a false statement where checked, and 3 results in a true statement.

Solution is {3}

But why does 0 result as an extraneous solution? We squared both sides of the equation, leaving it balanced.