Question

Given the equation Square root of 2x plus 1 = 3, solve for x and identify if it is an extraneous solution. (2 points)

Answer 1

Answer:

The correct answer is:

              x = 4, solution is not extraneous

Step-by-step explanation:

Extraneous solution--

It is the solution which is obtained from the equation i.e. by solving the equation but is not a valid solution to the equation.

True solution--

It is the solution which is obtained from the equation i.e. by solving the equation and is  a valid solution to the equation.

Here we have the equation as:

          $\sqrt{2x+1}=3$

Now on squaring both the sides of the equation we have:

$(\sqrt{2x+1})^2=3^2\\\\2x+1=9\\\\2x=9-1\\\\2x=8\\\\x=\dfrac{8}{2}\\\\x=4$

and the solution is a valid solution since the square root function is defined for this value of x.

Hence, the solution is not a extraneous solution i.e. it is a true solution to the equation.

Answer 2

ANSWER

x = 4, solution is not extraneous

EXPLANATION

The given equation is

$\sqrt{2x + 1} = 3$

Square both sides of the equation.

$2x + 1 = 9$

Group similar terms,

$2x = 9 - 1$

$2x = 8$

Divide both sides by 2.

$x = 4$

Check

Put x=4 into the original equation.

$\sqrt{2(4) + 1} = 3$

$\sqrt{9} = 3$

$3 = 3$

This statement is true.

Hence x=4 is not an extraneous solution.

Second choice is correct.