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Thread: Another Binomial theorem

  1. #1
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    Another Binomial theorem

    By assuming $\displaystyle 0<\sqrt{5}-2<\frac{1}{4}$ , deduce that the difference between $\displaystyle (\sqrt{5}+2)^5$ and an integer is less than $\displaystyle \frac{1}{1024}$
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  2. #2
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    Quote Originally Posted by thereddevils View Post
    By assuming $\displaystyle 0<\sqrt{5}-2<\frac{1}{4}$ , deduce that the difference between $\displaystyle (\sqrt{5}+2)^5$ and an integer is less than $\displaystyle \frac{1}{1024}$

    These are what i can think of :

    $\displaystyle 0+4<\sqrt{5}-2+4<\frac{1}{4}+4$

    $\displaystyle 4<\sqrt{5}+2<\frac{5}{4}$

    $\displaystyle 4^5<(\sqrt{5}+2)^5<(\frac{17}{4})^5$

    BUt i still don see the solution to these question .
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