Try out some values of x x .

Algebra Level 4

Find the largest positive real number x x such that

2 x = 1 x + 1 2 x \frac{2}{x} = \frac{1}{\lfloor x \rfloor} + \frac{1}{\lfloor 2x \rfloor}

where x \lfloor x \rfloor denotes the greatest integer less than or equal to x x .

Give your answer to 3 decimal places.


The answer is 2.857.

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