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Equation 1 :⌊x⌋+⌊2x⌋+⌊4x⌋=13 Equation 2 :⌊x⌋+⌊2x⌋+⌊4x⌋+⌊8x⌋=13\begin{aligned} \text{ Equation 1 }: &&\quad \lfloor x \rfloor + \lfloor 2 x \rfloor + \lfloor 4x \rfloor = 13 \\ \text{ Equation 2 }: &&\quad \lfloor x \rfloor + \lfloor 2 x \rfloor + \lfloor 4x \rfloor+ \lfloor 8x \rfloor = 13 \end{aligned} Equation 1 : Equation 2 :⌊x⌋+⌊2x⌋+⌊4x⌋=13⌊x⌋+⌊2x⌋+⌊4x⌋+⌊8x⌋=13
Do the equations above have real solutions?
Notation: ⌊⋅⌋ \lfloor \cdot \rfloor ⌊⋅⌋ denotes the floor function.
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