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Algebra2

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1.2x^2/3+5^1/3=12

2. 6x^6/3-5x^1/3-6=0

  • Algebra2 - ,

    #1
    2x^(2/3) + 5x^(1/3) = 12 , you have a typo
    let x^(1/3) = y
    your equation becomes

    2y^2 + 5y - 12 = 0
    (2y-3)(y+4) = 0
    y = 3/2 or y = -4

    then x^(1/3) = 3/2 ---- x = 27/8
    if x^(1/3) = -4 ----> x = -64

    check:
    if x = 27/8
    LS = 2(27/8)^(2/3) + 5(7/8)^(1/3)
    = 2(9/4) + 5(3/2)
    = 9/2 + 15/2 = 12 = RS

    if x = -64
    LS = 2(-64)^(2/3) + 5(-64)^(1/3)
    = 2(16) - 5(-4)
    ≠ RS

    x = 27/8

    (in y = x^(1/3) , x would be defined as x>0

    enter 2x^(2/3)+5x^(1/3)-12 into "first graph" of
    http://rechneronline.de/function-graphs/
    to see what I mean. There will be only one solution at x = 27/8 )

    ----------

    I think you have a typo in #2 if the question is supposed to be the same type
    It should probably say
    6x^(2/3) - 5x^(1/3) - 6 = 0

    try #2 in the same way by letting y = x^(1/3)
    it also factors, remember to reject a negative value of y

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