Question

Ex. 2 si 3 va rog

:D

Answer 1

2. 3x-2 < si egal 4
3x<si egal 6
x<si egal 2
x={0,1,2}

Answer 2

3) x=nr necunoscut
Transformam numerele periodice in fractii :
0,(3)=3/9=1/3
1,4(6)=(146-14)/90=132/90
0,(45)=45/99

2x-0,(3)=2x-1/3=(6x-1)/3
(6x-1)/3:1,4(6)=0,(45)
(6x-1)/3:132/90=45/99
<=>(6x-1)/3•90/132=5/11
<=>90(6x-1)/3•132=5/11
11•90•(6x-1)=3•132•5
990•(6x-2)=1980/:990
6x-1=2<=>6x=3=>x=3/6=1/2
=>x=0,5

2) A={x€R / |3x-2|<= 4}
AΠN=?( Π= intersectat)

|3x-2|<= -4 => -4<=3x-2<=4/ +2
<=>-2<=3x<=6/ :3 <=>-2/3<=x<=2
Deci x € intrvalului [-2/3;2]
*din aceste numere doar {0,1,2} sunt numere naturale
Deci AΠN={0,1,2}