Question

Solve for any extraneous solution(s)
√1-3x = √x+11

Answer 1

x= - 2.5.

Explanation:

First, let's isolate one of the square roots. We can do this by squaring both sides of the equation:

(√1-3x)^2 = (√x+11)^2

1-3x = x+11

Now, we can solve for x:

1-3x = x+11

-4x = 10

x = -2.5

We obtained a valid solution for x, but we need to check if it is an extraneous solution.

To do this, we need to substitute x=-2.5 back into the original equation and check if it satisfies the equation:

√1-3x = √x+11

√1-3(-2.5) = √(-2.5)+11

√8.5 ≈ 2.92

√8.5 ≈ 2.92 is a valid solution, so we don't have any extraneous solutions.

Therefore, the only solution to the equation is x=-2.5.