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Math Help - approximation

  1. #1
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    approximation

    Write down the first three terms in the binomial expansion of \sqrt[4]{1+\frac{x}{81}}
    Here i got

    1+\frac{x}{324}-\frac{x^2}{69984}

    Then deduce that \sqrt[4]{80}=2.9907 .. not sure with this part

    That should be the approximation sign , i am not sure how to do it with latex .
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  2. #2
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    Quote Originally Posted by thereddevils View Post
    Write down the first three terms in the binomial expansion of \sqrt[4]{1+\frac{x}{81}}
    Here i got

    1+\frac{x}{324}-\frac{x^2}{69984}

    Then deduce that \sqrt[4]{80}=2.9907 .. not sure with this part

    That should be the approximation sign , i am not sure how to do it with latex .
    Note that \sqrt[4]{1+\frac{x}{81}} = \sqrt[4]{\frac{81+x}{81}} = \frac{1}{3} \sqrt[4]{81+x} so substitute x = -1 into the approximate expansion of \sqrt[4]{1+\frac{x}{81}} and then re-arrange to get the approximate value of \sqrt[4]{80}.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Note that \sqrt[4]{1+\frac{x}{81}} = \sqrt[4]{\frac{81+x}{81}} = \frac{1}{3} \sqrt[4]{81+x} so substitute x = -1 into the approximate expansion of \sqrt[4]{1+\frac{x}{81}} and then re-arrange to get the approximate value of \sqrt[4]{80}.

    THank you .
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