Question

Aflati multimea tuturor perechilor de numere intrege care verifica simultant relatiile: |x-1|=1 si |y-x|<2
Ajutor va rog ....îmi trb urgent

Answer 1

|x - 1| = 1 => x₁ - 1 = -1, deci x₁ = 0, sau x₂ - 1 = 1. deci x₂ = 2.

| y₁ - x₁ | < 2, sau | y₁ - 0 | < 2, sau | y₁ | < 2, deci -2 < y₁ < 2, deci y ∈ (-2,2) ∩ Z => y ∈ {-1,0,1}.

Perechile ar fi (x,y) = {(0,-1), (0,0), (0,1)}

| y₂ - x₂ | < 2, sau | y₂ - 2 | < 2, sau | y₂ - 2 | < 2, deci -2 < y₂ - 2 < 2, deci y ∈ (0,4) ∩ Z => y ∈ {1,2,3}.

Perechile ar fi (x,y) = {(2,1), (2,2), (2,3)}.

Green eyes.