Using the equation
, are both x = 2 and x = 9 solutions or are one/both of them extraneous solutions? Explain.​

Given:

The equation is:

To find:

Whether and both are solutions or one/both of them extraneous solutions.

Solution:

We have,

Subtract 5 from both sides.

Taking square on both sides, we get

Splitting the middle term, we get

Now, substitute in the given equation.

This statement is false because . So, 2 is an extraneous solution.

Substitute in the given equation.

This statement is true. So, 9 is a solution of given equation.

Therefore, 2 is an extraneous solution and 9 is a solution of given equation.