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Math Help - Prove the following solutions..

  1. #1
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    Prove the following solutions..

    a) show that x^(-2/3) = 1/2 is x= square root (8)

    b) 2x^3 - 3x^2 - 8x +12 = 0 are x = -2,2, 3/2

    *dont just put the values of x into the equation..you need to prove itt
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  2. #2
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    Quote Originally Posted by yess View Post
    a) show that x^(-2/3) = 1/2 is x= square root (8)

    b) 2x^3 - 3x^2 - 8x +12 = 0 are x = -2,2, 3/2

    *dont just put the values of x into the equation..you need to prove itt
    For the first one, consider what happens when you raise both sides to (-3/2).
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  3. #3
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    b) 2x^3 - 3x^2 - 8x + 12 = 2x^3 - 8x - 3x^2 + 12

    = 2x(x^2 - 4) - 3(x^2 - 4)

     = (x^2 - 4)(2x - 3)

     = (x-2)(x +2)(2x - 3).


    Therefore if

    2x^3 - 3x^2 - 8x + 12 = 0

    (x-2)(x+2)(2x-3) = 0

    x - 2 = 0 or x+2 = 0 or 2x - 3 = 0

    x = 2 or x = -2 or x = \frac{3}{2}.
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