Question

14 Determinați mulțimile: a A={(x,y) = ZxZ 88+ xy = 33); c C = ((x,y) e NxN xy + 2x+4y=22); b B=((x,y) e NxN xy-3x-3y=5]: d D= ((x,y) = NxN 3x+7y=60).​
ajutor va rog

Answer 1

Explicație pas cu pas:

a)

88 + xy = 33

xy = 33 - 88

xy = -55

$\mathcal{D}_{55} = \Big\{-55; -11; -5; -1; 1; 5; 11; 55\Big\}$

x = -55 => y = 1

x = -11 => y = 5

x = -5 => y = 11

x = -1 => y = 55

$A = \Big\{(-55;1), (-11;5), (-5;11), (-1;55), (1;-55), (5;-11), (11;-5), (55;-1)\Big\}$

c)

xy + 2x + 4y = 22

x(y + 2) = 2(11 - 2y)

=> 11 - 2y ≥ 0 => 2y ≤ 11 => y ≤ 5

y = 0 => 2x = 22 => x = 11

y = 1 => 3x = 18 => x = 6

y = 2 => 4x = 14 => x ∉ N

y = 3 => 5x = 10 => x = 2

y = 4 => 6x = 6 => x = 1

y = 5 => 7x = 2 => x ∉ N

$C = \Big\{ (1;4), (2;3), (6;1), (11;0) \Big\}$

d)

3x + 7y = 60

7y = 3(20 - x)

=> 3x ≤ 60 <=> x ≤ 20 și 7y ≤ 60 <=> y ≤ 8

y este multiplu de 3 => y ∈ {0, 3, 6}

y = 0 => x = 20

y = 3 => x = 13

y = 6 => x = 6

$D = \Big\{ (6;6), (13;3), (20;0) \Big\}$