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17 January, 18:07

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.

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  1. 17 January, 18:19
    0
    √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.
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