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2 [x] {x} = x^2 - 3/2 x - 11/16

Source: 2022 Moldova JBMO TST p10

November 4, 2022
algebrafloor function

Problem Statement

Solve in the set RR the equation 2⋅[x]⋅{x}=x2−32⋅x−11162 \cdot [x] \cdot \{x\} = x^2 - \frac32 \cdot x - \frac{11}{16} where [x][x] and {x}\{x\} represent the integer part and the fractional part of the real number xx, respectively.
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