Question

Given the equation square root of 2x+1=3 solve for x and identify if it is an extraneous solution

Answer 1

x=4 and I believe it is an extraneous solution, to see if it is extraneous or not

* put x=4 in the original given equation, to see if it satisfies , if not then the solution is not extraneous.

Answer 2

Answer:

Given the equation: $\sqrt{2x+1} =3$        ......[1]

Taking square both sides, we get;

$2x+1 = 3^2$

$2x+1 = 9$

Subtract 1 from both sides we get;

2x = 8

Divide both sides by 2 we get;

x = 4

Extraneous solution states that it is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation.

Substitute the value of x in [1] we get;

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

$\sqrt{8+1}=3$  

$\sqrt{9} =3$

$3 =3$   True.

Therefore, the value of x is 4 and it is not an extraneous solution.