# Floor Ceiling Ceiling Floor: JEE Style

Algebra Level 5

$\large \lceil x \lfloor x \rfloor \rceil + \lfloor x \lceil x \rceil \rfloor = 1729$

If the range of positive $$x$$ satisfy the equation above is $$\alpha \leq x \leq \beta$$.

What is the value of $$30\alpha + 29 \beta+1$$ if we know that it is an integer?

Inspired by: Floor Ceiling Ceiling Floor.

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