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Frctional part equation

  1. Sep 7, 2013 #1
    Calculation of Real ##x## in ##\{x\} = \{x^2\} = \{x^3\}##, Where ##\{x\} = ## fractional part of ##x##

    My Try:: We Know that ##\{x\} ## and ##\{x^2\}## and ##\{x^3\}## are are ##\in \left[0,1\right)##

    So Let we take ##\{x\} = \{x^2\} = \{x^3\} = k##, where ##k\in \left[0,1\right)##

    So If ##\{x\} = k## , Then ##x-\lfloor x \rfloor = k\Rightarrow x = \lfloor x \rfloor +k##

    where ##\lfloor x \rfloor = ## floor function of ##x##

    Similarly If ##\{x^2\} = k## , Then ##x^2-\lfloor x^2 \rfloor = k\Rightarrow x^2 = \lfloor x^2 \rfloor +k##

    Sililarly If ##\{x^3\} = k## , Then ##x^3-\lfloor x \rfloor = k\Rightarrow x^3 = \lfloor x^3 \rfloor +k##

    Now How Can I proceed after that,

    plz Help me

    Thanks
     
  2. jcsd
  3. Sep 7, 2013 #2

    verty

    User Avatar
    Homework Helper

    Hint: test some values for k.
     
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