Which statements describe the solutions to (√x-2)-4=x-6? Check all that apply. There are no true solutions to the radical equat

Question

Which statements describe the solutions to (√x-2)-4=x-6? Check all that apply.

There are no true solutions to the radical equation.
x = 2 is an extraneous solution.
x = 3 is a true solution.
There is only 1 true solution to the equation.
The zeros of 0 = x2 – 5x + 6 are possible solutions to the radical equation.

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Eva 2 weeks 2021-11-20T20:00:54+00:00 2 Answers 0

Answers ( )

    0
    2021-11-20T20:02:14+00:00

    Answer:

    x = 3 is a true solution.

    The zeros of 0 = x2 – 5x + 6 are possible solutions to the radical equation.

    Step-by-step explanation:

    Given in the question an equation,

    √(x-2) – 4 = x – 6

    √(x-2) = x – 6 + 4

    √(x-2) = x -2

    Take square on both sides of the equation

    √(x-2)² = (x -2)²

    x – 2 = x² – 4x + 4

    0 = x² – 4x – x + 4 + 2

    0  = x² – 5x + 6

    a = 1

    b = -5

    c = 6

    x = -b±√(b²-4ac) / 2a

    x = -(-5)±√(5²-4(1)(6)) / 2(1)

    x = 5 ± √1 / 2

    x = 5 + 1 / 2 or  5 – 1 /2

    x = 3 or x = 2

    Plug value of x in the radical equation:

    x=3

    √(3-2)-4=3-6

    √1 -4 = -3

     1 – 4 = -3

        -3 = -3

    x=2

    √(2-2)-4=2-6

    0 – 4 = -4

        -4 = -4

    0
    2021-11-20T20:02:26+00:00

    Answer:

    C. x = 3 is a true solution.

    E. The zeros of 0 = x2 – 5x + 6 are possible solutions to the radical equation.

    Step-by-step explanation:

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