# Functions

Algebra Level 5

If $$x_{1},x_{2},x_{3}$$ are real roots of the equation $${\frac{1}{[x]}+\frac{1}{[2x]}=\{x\}+\frac{1}{3}}$$, find $$x_{1}+x_{2}+x_{3}$$

Note: $$[.]$$ denotes greatest integer function and $$\{.\}$$ denotes fractional part of $$x$$.

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