savannahsisla
contestada

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

Respuesta :

kudzordzifrancis

ANSWER

x = 4, solution is not extraneous

EXPLANATION

The given equation is

[tex] \sqrt{2x + 1} = 3[/tex]

Square both sides of the equation.

[tex]2x + 1 = 9[/tex]

Group similar terms,

[tex]2x = 9 - 1[/tex]

[tex]2x = 8[/tex]

Divide both sides by 2.

[tex]x = 4[/tex]

Check

Put x=4 into the original equation.

[tex] \sqrt{2(4) + 1} = 3[/tex]

[tex] \sqrt{9} = 3[/tex]

[tex]3 = 3[/tex]

This statement is true.

Hence x=4 is not an extraneous solution.

Second choice is correct.

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:

          [tex]\sqrt{2x+1}=3[/tex]

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

[tex](\sqrt{2x+1})^2=3^2\\\\2x+1=9\\\\2x=9-1\\\\2x=8\\\\x=\dfrac{8}{2}\\\\x=4[/tex]

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.

ACCESS MORE
ACCESS MORE
ACCESS MORE
ACCESS MORE

Otras preguntas