Question

Which statement best reflects the solution(s) of the equation? √3x+1 −x+3=0 (note it's the square root of 3x+1)
a. There is only one solution: x = 8. The solution x = 1 is an extraneous solution.
b. There is only one solution: x = 8. The solution x = 0 is an extraneous solution.
c. There is only one solution: x = 1. The solution x = 8 is an extraneous solution.
d. There are two solutions: x = 1 and x = 8.

Answer 1

Hello there!

The correct answer is option A
There is only one solution x= 8. The solution x=1 is an extraneous solution.

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Check the picture below for steps

Answer 2

There is only one solution: x = 8. The solution x = 1 is an extraneous solution.

We have;

√3x+1 −x + 3 =0

So;

√3x+1 = -(−x + 3)

√3x+1 = x - 3

3x+1 = ( x - 3)^2

3x+1 = x^2 - 6x + 9

Then

x^2 - 9x + 8 = 0

We now have to solve the quadratic  equation to obtain;

x=8 or x=1

Now plug back x =1 into the original equation;

√3x+1 −x + 3 =0

√3(1) + 1 - (1) + 3 = 4

Plug back x = 8

√3(8) + 1 - 8 + 3 = 0

Hence, there is only one solution: x = 8. The solution x = 1 is an extraneous solution.

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