SOLUTION: Which statement best reflects the solution(s) of the equation? The equation and answer choices are in the link here: https://prnt.sc/le2sbh A. There is only one solution: x =

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Which statement best reflects the solution(s) of the equation? The equation and answer choices are in the link here: https://prnt.sc/le2sbh A. There is only one solution: x =      Log On


   

Question 1127948: Which statement best reflects the solution(s) of the equation?
The equation and answer choices are in the link here: https://prnt.sc/le2sbh
A. There is only one solution: x = 8.
The solution x = 1 is an extraneous solution.
B. There are two solutions: x = 1 and x = 8.
C. There is only one solution: x = 8.
The solution x = 0 is an extraneous solution.
D.There is only one solution: x = 1.
The solution x = 8 is an extraneous solution.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283x%2B1%29-x%2B3=0
sqrt%283x%2B1%29=x-3
%28sqrt%283x%2B1%29%29%5E2=%28x-3%29%5E2
3x%2B1=x%5E2-6x%2B9
0=x%5E2-6x-3x-1%2B9
x%5E2-9x%2B8=0
x%5E2-8x-x%2B8=0
%28x%5E2-8x%29-%28x-8%29=0
x%28x-8%29-%28x-8%29=0
%28x-1%29%28x-8%29=0
x=1-> because sqrt%283%2A1%2B1%29%3E0 we cannot use this solution
x=8=>so, only solution we can use

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%283x%2B1%29-x%2B3%29+

your answer is: A. There is only one solution: x+=+8.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


sqrt%283x%2B1%29-x%2B3+=+0

Isolate the radical

sqrt%283x%2B1%29+=+x-3

Square both sides to get rid of the radical

3x%2B1+=+x%5E2-6x%2B9

Solve the quadratic equation by factoring

x%5E2-9x%2B8+=+0
%28x-8%29%28x-1%29+=+0

The two possible solutions are x=8 and x=1.

Because we squared both sides of the equation at one point, there might be extraneous roots. So see if each of the possible roots satisfies the original equation.

x=8: sqrt%2825%29-8%2B3+=+5-8%2B3+=+0 YES

x=1: sqrt%284%29-1%2B3+=+2-1%2B3+%3C%3E0 NO

Note if we had been able to use -2 as the square root of 4, the equation would have been satisfied: -2-1+3 = 0. This will usually (maybe always, I'm not sure) be the case when you solve a radical equation like this and one of the roots is extraneous.

ANSWER: Choice A: one solution, x=8; x=1 is extraneous