Ivan Shishkin, Rye (1878)

Problems/Real analysisExerciseUnreviewed

An equation involving the floor function 2

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28
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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  1. Determine the set of real numbers xx such that
    ⌊x2+2x+1⌋=0.\lfloor x^2+2x+1\rfloor=0.
  2. Determine the set of real numbers yy such that
    ⌊y2⌋+2⌊y⌋+⌊1⌋=0.\lfloor y^2\rfloor + 2\lfloor y\rfloor +\lfloor 1\rfloor=0.3) Compare the two sets obtained. Are they the same?
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