Question

Which of the following equations will have an extraneous solution?

Answer 1

When you square a radical equation you sometimes get a solution to the squared equation that is not a solution to the original equation. Such an equation is called an extraneous solution.

One must always check the solution in the original equation to discard extraneous solutions.

The first equation is:

`\sqrt[]{x}=2`

Squaring:

x = 4

Checking the solution:

`\sqrt[]{4}=2`

The solution is correct.

The second equation is:

`\sqrt[]{x}=-2`

Squaring:

x = 4

When we check the solution

`\sqrt[]{4}=2`

It does not check correctly unless we consider the double sign of a square root. Thus this last equation has an extraneous solution