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(4x)^2/3=(30x+4)^1/3
please explain=)

  • math -

    (4x)^(2/3) = (30x+4)^(1/3)
    To do this, note that it's much easier to work with whole number exponents. This we raise both side terms by 3, so that the denominator 3 will be cancelled:
    (4x)^(2/3 * 3) = (30x+4)^(1/3 * 3)
    (4x)^2 = (30x+4)^1
    16x^2 = 30x + 4
    Solving for x,
    8x^2 - 15x - 2 = 0
    (8x + 1)(x - 2) = 0
    x = 2
    x = -1/8
    Then we check by substituting these x values to the original equation:
    i. x = 2
    (4x)^(2/3) = (30x+4)^(1/3)
    (4*2)^(2/3) = (30*2+4)^(1/3)
    (8)^(2/3) = 64^(1/3)
    2^2 = 4
    4 = 4
    Thus x is indeed equal to 2.

    ii. x = -1/8
    (4x)^(2/3) = (30x+4)^(1/3)
    (4*(-1/8))^(2/3) = (30*(-1/8)+4)^(1/3)
    (-1/2)^(2/3) = (-15/4 + 16/4)^(1/3)
    (1/4)^(1/3) = (1/4)^(1/3)
    Thus x is also equal to -1/8.

    Hope this helps~ :3

  • math -

    i didn't get how 16x^2 turned into 8x^2

    16x^2 = 30x + 4
    Solving for x,
    8x^2 - 15x - 2 = 0

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