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[x^2 - 2x] + 2[x] = [x]^2

Source: 2003 Swedish Mathematical Competition p3

March 21, 2021
floor functionalgebraequation

Problem Statement

Find all real solutions xx of the equation ⌊x2−2⌋+2⌊x⌋=⌊x⌋2.\lfloor x^2-2 \rfloor +2 \lfloor x \rfloor = \lfloor x \rfloor ^2. .
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