Question

Which statement describes if there is an extraneous solution to the equation √x-3 = x-5?

Answer 1

Remember that an extraneous solution of an equation, is the solution that emerges from solving the equation but is not a valid solution.

Lets solve our equation to find out what is the extraneous solution:

and

and

So, the solutions of our equation are and . Lets replace each solution in our original equation to check if they are valid solutions:

- For

We can conclude that 7 is a valid solution of the equation.

- For

We can conclude that 4 is not a valid solution of the equation; therefore, 4 is a extraneous solution.

We can conclude that the correct answer is: D. the extraneous solution is x = 4

Explanation:

Answer 2

the extraneous solution is x = 4