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.

Question

Mathematics

Mara Kline

16 March, 11:29

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.

+3

Answers (1)

Know the Answer?

Jaylah Goodman · Answer 1

√3x+1 - x+3=0

(√3x+1) ^2 = (x-3) ^2

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

0 = x^2 - 9x + 8

0 = (x - 8) (x - 1)

X = 8 and x = 1

First let’s solve for x = 8

√3 (8) + 1 - (8) + 3 = 0

√24 + 1 - 5 = 0

√25 - 5 = 0

5-5=0

0=0

X=8 is a solution

For x=1

√3 (1) + 1 - (1) + 3 = 0

√4 - 4 = 0

2 - 4 = 0

-2=0

X=1 is not a solution

Therefore:

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