MathDB
Equation with floor function

Source: Romanian District Olympiad 2023 9.2

March 11, 2023
algebrafloor function

Problem Statement

[*]Determine all real numbers xx{} satisfying ⌊x⌋2−x=−0.99\lfloor x\rfloor^2-x=-0.99. [*]Prove that if a⩽−1a\leqslant -1, the equation ⌊x⌋2−x=a\lfloor x\rfloor^2-x=a does not have real solutions.
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