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)

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.