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Math Help - textbook isn't helping me with this problem can anybody help

  1. #1
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    textbook isn't helping me with this problem can anybody help

    ^5 square root of 5x-5 = ^5 square root of 6x-7

    the ^ 5 is the little 5 on top before the square root symbol. I'm having trouble finding out how to solve for x
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  2. #2
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    \displaystyle \sqrt[5]{5x-5} = \sqrt[5]{6x - 7}

    \displaystyle (\sqrt[5]{5x-5})^5 = (\sqrt[5]{6x-7})^5

    \displaystyle 5x-5=6x-7.

    Go from here.
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  3. #3
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    If x^n = y^n, then x = y, of course.
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  4. #4
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    x^n = y^n sometimes has more solutions than just x = y.
    Simplest example: x^2 = y^2 could be x = -y

    Also, when raising to a power, we may actually have fewer solutions:
    Consider sqrt(x) = -sqrt(y), squaring both sides gives x = y, but
    sqrt(x) = -sqrt(x) is only true when x=0.
    It is always a good idea to plug solutions back into the original equation to check.

    For this problem, all solutions check out.
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  5. #5
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    Quote Originally Posted by snowtea View Post
    x^n = y^n sometimes has more solutions than just x = y.

    Simplest example: x^2 = y^2 could be x = -y
    If \displaystyle n is odd, this is true, at least for real solutions.
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