Frctional part equation

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