Question

Aflati numerele naturale stiind ca:
a) (2x-3) |9
b)(4x+1) |20
c)18
___
2x+1
d) 22
____
X-2

Answer 1

a) (2x - 3) ∈ {1, 3, 9}
2x - 3 = 1
2x = 4
x = 2

2x - 3 = 3
2x = 6
x = 3

2x - 3 = 9
2x = 12
x = 12:2 = 6
x∈{2, 3, 6}

b) (4x + 1) ∈ {1, 2, 4, 5, 10, 20}
4x + 1=1
4x = 0
x = 0

4x + 1 = 2
4x = 1
x = 1/4∉N

4x + 1 = 4
4x = 3
x = 3/4∉N

4x + 1 = 5
4x = 4
x = 1

4x + 1 = 10
4x = 9
x = 9/4∉N

4x + 1 = 20
4x = 19
x = 19/4 ∉N

x∈{0, 1}

c) (2x + 1) ∈ {1, 2, 3, 6, 9, 18}
2x + 1 = 1
2x = 0
x = 0

2x + 1 = 2
2x = 1
x = 1/2 ∉ N

2x + 1 = 3
2x = 2
x = 1

2x + 1 = 6
2x = 5
x = 5/2 ∉ N

2x + 1 = 9
2x = 8
x = 4

2x + 1 = 18
2x = 17
x = 17/2 ∉ N

x ∈ {0, 1, 4}

d) (x - 2) ∈ {1, 2, 11, 22}
x - 2 = 1
x = 3

x - 2 = 2
x = 4

x - 2 = 11
x = 13

x - 2 = 22
x = 24

x∈{3, 4, 13, 24}