Question

exercițiul este in poza​

Answer 1

Explicație pas cu pas:

a)

x | 15 => x ∈ {1, 3, 5, 15} ∈ N*

b)

x | (x + 7)

x | x => x | 7 => x ∈ {1, 7} ∈ N*

c)

x | (5x + 9)

x | 5x => x | 9 => x ∈ {1, 3, 9} ∈ N*

d)

(x + 1) | (x + 5) <=> (x + 1) | [(x + 1) + 4]

(x + 1) | (x + 1) => (x + 1) | 4

=> (x + 1) ∈ {1, 2, 4} | (-1) => x ∈ {0, 1, 3}

x ∈ N* => x ∈ {1, 3}

e)

(x + 3) | (3x + 18) <=> (x + 3) | [3(x + 3) + 9]

(x + 3) | 3(x + 3) => (x + 3) | 9

=> (x + 3) ∈ {1, 3, 9} | (-3) => x ∈ {-2, 0, 6}

x ∈ N* => x = 6

f)

(x + 2) | (4x + 13) <=> (x + 2) | [4(x + 2) + 5]

(x + 2) | 4(x + 2) => (x + 2) | 5

=> (x + 2) ∈ {1, 5} | (-2) => x ∈ {-1, 3}

x ∈ N* => x = 3