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math

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Solve. Check for extraneous solutions.

1) (/3x+7) = x-1


2) (3/2x)-3=9




Note: (/3x+7) is the square root of 3x plus 7 and (3/2x)-3=9 is 3 times the square root of 2x - 3 equals 9.

  • math - ,

    1. sqrt(3x+7) = x-1.
    Square both sides:
    3x + 7 = x^2 - 2x + 1.
    -x^2 + 2x +3x = 1 - 7 = - 6.
    Multiply both sides by -1:
    x^2 -2x -3x = 6.
    x^2 - 5x - 6 = 0.
    (x+1)(x-6) = 0.

    x+1 = 0.
    X = -1. Does not satisfy original Eq.

    x-6 = 0.
    X = 6.

    2. 3*sqrt(2x) - 3 = 9.
    3*sqrt(2x) = 9+3 = 12.
    Divide both sides by 3:
    sqrt(2x) = 4.
    Square both sides:
    2x = 16.
    X = 8.

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