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math-radical equations

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Here's one of the questions I have problems with:
cube root of (x+2)=6th root of (9x+10)
A. -1, 6
B. [-13 +/- sqrt(193)]/2
C. 1, -6
D. [13 +/- sqrt(145)]/2

Please explain how to solve this. Should you cube both sides, or raise both to the 6th? and I get lost trying to do more than square a radical. i'd show my "work" which is basically nonsense but it's useless because I honestly have no idea how to solve this.
thanks in advance for the help. having an example of how to solve these kinds of problems would help me a lot, so if you can step by step would be great.

  • math-radical equations - ,

    sorry to post twice; computer meltdown...

  • math-radical equations - ,

    (x+2)^(1/3) = (9x+10)^(1/6)
    raise both sides to the sixth
    [ (x+2)^(1/3) ] ^6 = (x+2)^2
    [ (9x+10)^(1/6)]^6 = (9x+10)^1 = 9x+10
    so
    x^2 + 4 x + 4 = 9 x + 10
    x^2 -5 x - 6 = 0
    (x-6)(x+1) = 0
    x = 6 or x = -1

  • math-radical equations - ,

    it really helps to write 15th root of x for example as x^(1/15) power

  • math-radical equations - ,

    Oh, and always check the answers
    in this case you have for x = -1
    1^1/3 = 1^1/6 yes, ok
    and for x = 6
    8^1/3 = 64^1/6 ? = (8*8)^1/6 =(2*2*2*2*2*2)^1/6 = 2
    2 = 2 sure enough

  • math-radical equations - ,

    LOL, if I had really noticed it was multiple choice I would have tried x = -1 immediately :)

  • math-radical equations - ,

    thanks, Damon - you are awesome =)

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