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Math Help - Unusual equation

  1. #1
    Senior Member Twig's Avatar
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    Unusual equation

    Hi!

    How should one proceed with an equation like this..

    x^(1/2) + x^(1/4) = 20

    without having any calculator obv..

    thanks!
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  2. #2
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    let  y = x^{\frac{1}{4}}

    your equation becomes

    y^2 + y - 20 = 0

    factor (y+5)(y-4)=0

    can you take it form here?
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  3. #3
    Senior Member Twig's Avatar
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    hi

    uh..
    I understood what you did.

    y = -5 or y = 4 ?

    but.. do I get the correct answer?
    If I insert 4 into the original equation..
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  4. #4
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    Because x^{\frac{1}{4}}  =  - 5 is impossible the there is one solution.
    x^{\frac{1}{4}}  = 4\quad  \Rightarrow \quad x = 64
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  5. #5
    Senior Member Twig's Avatar
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    hi

    doesnt x = 256 ?

    because 4^4 is 256

    and sqrt of 256 is 16, so 16 plus 4 = 20
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  6. #6
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    Quote Originally Posted by Twig View Post
    doesnt x = 256 ?

    because 4^4 is 256

    and sqrt of 256 is 16, so 16 plus 4 = 20
    Yes.

    Plato made a simple careless mistake. Be that as it may, it's a mere detail - it's the method that's important and the method is what Plato's given you.
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  7. #7
    Senior Member Twig's Avatar
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    hi

    Absolutely, the method is def. the most important.
    Just wanted to be sure that I got it correct.

    Thanks!
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