Question

Radical sign 2x+8-6=3
Is the solution extraneous or not extraordinary

Answer 1

Radical sign 2x+8-6=3  Is the non-extraneous solution.

Given: The equation: $\sqrt{2x + 8} - 6=3$

What are extraneous solutions?

For a given equation, where x is a variable after finding the solution for x which can be 1 or more values, when need to place each of the solution in the equation and need to check if the value(s) satisfy the given equation. If a solution satisfies the given solution then the solution is said to be non-extraneous and if it does not satisfy the given equation it is said to be extraneous solution.

Let's solve the given question.

Solving the equation:

Adding -6 on both  sides, we get:

$\sqrt{2x + 8} - 6 + 6=3+ 6$

$\sqrt{2x + 8} =9$

Squaring both sides

$(\sqrt{2x + 8})^2 =9^2$

2x + 8 = 81

2x = 73

x = 73 / 2

Now to check if the solution is extraneous or not, we need to place the value of x = 73 / 2 in the given equation. So,

x: 73 / 2

$\sqrt{2*\frac{73}{2} + 8} - 6=3$

$\sqrt{73 + 8} - 6=3$

$\sqrt{81 } - 6=3$

9 - 6 = 3

3 = 3

Therefore, x = 73 / 2 is a true solution for the given equation.

Hence, the solution for the equation $\sqrt{2x + 8} - 6=3$ is non-extraneous.

Know more about "extraneous solutions" here: https://brainly.com/question/14054707

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Disclaimer: The question is incomplete. The complete question is mentioned below:

$\sqrt{2x + 8} - 6=3$

Is the solution extraneous or non-extraneous