Question

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

x = 4, solution is extraneous
x = 4, solution is not extraneous
x = 5, solution is extraneous
x = 5, solution is not extraneous

Answer 1

The correct answer is:

x = 4, solution is not extraneous

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:

`√(2x+1)=3`

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

`(√(2x+1))^2=3^2\\\\2x+1=9\\\\2x=9-1\\\\2x=8\\\\x=(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

x = 4, solution is not extraneous

EXPLANATION

The given equation is

`√(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.

`√(2(4) + 1) = 3`

`√(9) = 3`

`3 = 3`

This statement is true.

Hence x=4 is not an extraneous solution.

Second choice is correct.