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24. a) A= { x∈IN I _12_ ∈ IN} c) C={x∈Z I _15_ ∈Z}
x x-2
12:x∈ IN 15:(x-2) ∈Z (x-2)=y
x∈{1;2;3;4;6;12} 15:y
y∈{+/-1; +/-3.; +/-5; +/-15}
x-2= 1 x- 2= -1 x- 2= 3 x-2= -3
x= 3 x=1 x= 5 x=-1
x- 2= 5 x-2= - 5 x-2=15 x- 2= -15
x= 7 x= -3 x=17 x= -13
x∈{+/-1;+/-3; 5;7;-13;17.}
d) D={x∈Z I _18_ ∈Z} e) E={x∈IN I_28_∈IN}
x-1 x+1
18:(x-1) , x-1=y 28:(x+1) , x+1=y
18:y 28:y
y∈{+/-1;+/-2;+/-3;+/-6;+/-9;+/-18} y∈{1;2;4;7;14;28}
x-1= 1 x- 1= -1 x+ 1= 1 x+ 1= 2
x= 2 x= 0 x= 0 x= 1
x-1= 2 x- 1= -2 x+ 1= 4 x+ 1= 7
x= 3 x= -1 x= 3 x= 6
x-1= 3 x- 1= -3 x+ 1=14 x+ 1= 28
x= 4 x= -2 x= 10 x= 27
x-1= 6 x- 1= -6 x∈{0;1; 3; 6; 10; 27.}
x= 7 x= -5
x-1= 9 x- 1= -9
x= 10 x= -8
x-1=18 x- 1= -18
x= 19 x= -17
x∈{-17;-8;-5;-2;-1;0;2;3;4;7;10;19.}
f) F={x∈ZI _35_ ∈ Z} g) G={x∈ZI _45_ ∈Z}
2x-1 2x+1
35:(2x- 1) , 2x- 1= y 45:(2x+ 1) , 2x+ 1= y
35:y , y∈{+/-1;+/- 5;+/-7; +/- 35} 45:y y∈{+/-1;+/- 5;+/-9;+/-45}
2x- 1= 1 2x- 1= -1 2x+ 1= 1 2x+ 1= -1
x= 1 x=0 x= 0 x= -1
2x- 1= 5 2x- 1= -5 2x+ 1= 5 2x+ 1= -5
x= 3 x=-2 x= 2 x= -3
2x- 1= 7 2x- 1= -7 2x+ 1= 9 2x+ 1= -9
x= 4 x=-3 x= 4 x= -5
2x- 1= 35 2x- 1= -35 2x+ 1= 45 2x+ 1= -45
x= 18 x=-17 x= 22 x= -23
x∈ {-17;-3;-2;0;1;3;4;18.} x∈{-23; -5;-3;-1;0;2;4;22
F={x∈ZI _35_ ∈ Z} g) G={x∈ZI _45_ ∈Z}
2x-1 2x+1
35:(2x- 1) , 2x- 1= y 45:(2x+ 1) , 2x+ 1= y
35:y , y∈{+/-1;+/- 5;+/-7; +/- 35} 45:y y∈{+/-1;+/- 5;+/-9;+/-45}
2x- 1= 1 2x- 1= -1 2x+ 1= 1 2x+ 1= -1
x= 1 x=0 x= 0 x= -1
2x- 1= 5 2x- 1= -5 2x+ 1= 5 2x+ 1= -5
x= 3 x=-2 x= 2 x= -3
2x- 1= 7 2x- 1= -7 2x+ 1= 9 2x+ 1= -9
x= 4 x=-3 x= 4 x= -5
2x- 1= 35 2x- 1= -35 2x+ 1= 45 2x+ 1= -45
x= 18 x=-17 x= 22 x= -23
x∈ {-17;-3;-2;0;1;3;4;18.} x∈{-23; -5;-3;-1;0;2;4;22
i) I={x∈ZI _-25_ ∈ Z} j) J={x∈ZI _30_ ∈Z}
x-1 x-4
-25:(x- 1) , x- 1= y 30:(x- 4) , x- 4= y
-25:y , y∈{+/-1;+/- 5;+/- 25} 30:y, y∈{+/-1;+/- 2;+/-3;+/-5;+/-6;+/-10;+/-15;+/-30.}
x- 1= 1 x- 1= -1 x- 4= 1 x- 4= -1
x= 2 x=0 x= 5 x= 3
x- 1= 5 x- 1= -5 x- 4= 2 x- 4= -2
x= 6 x=- 4 x= 6 x= 2
x- 1= 25 x- 1= -25 x- 4= 3 x- 4= -3
x= 26 x=- 24 x= 7 x= 1
x∈ {-24;-4;0;2;6;26.} x- 4= 5 x- 4= -5
x= 9 x= -1
x- 4= 6 x- 4= -6
x= 10 x= -2
x- 4= 10 x- 4= -10
x= 14 x= - 6
x- 4= 15 x- 4= -15
x= 19 x= -11
x- 4= 30 x- 4= -30
x= 34 x= -26
x∈{-26;-11;-6;-2;-1;1;2;3;5;6;7;9;10;14;19;34.}
x x-2
12:x∈ IN 15:(x-2) ∈Z (x-2)=y
x∈{1;2;3;4;6;12} 15:y
y∈{+/-1; +/-3.; +/-5; +/-15}
x-2= 1 x- 2= -1 x- 2= 3 x-2= -3
x= 3 x=1 x= 5 x=-1
x- 2= 5 x-2= - 5 x-2=15 x- 2= -15
x= 7 x= -3 x=17 x= -13
x∈{+/-1;+/-3; 5;7;-13;17.}
d) D={x∈Z I _18_ ∈Z} e) E={x∈IN I_28_∈IN}
x-1 x+1
18:(x-1) , x-1=y 28:(x+1) , x+1=y
18:y 28:y
y∈{+/-1;+/-2;+/-3;+/-6;+/-9;+/-18} y∈{1;2;4;7;14;28}
x-1= 1 x- 1= -1 x+ 1= 1 x+ 1= 2
x= 2 x= 0 x= 0 x= 1
x-1= 2 x- 1= -2 x+ 1= 4 x+ 1= 7
x= 3 x= -1 x= 3 x= 6
x-1= 3 x- 1= -3 x+ 1=14 x+ 1= 28
x= 4 x= -2 x= 10 x= 27
x-1= 6 x- 1= -6 x∈{0;1; 3; 6; 10; 27.}
x= 7 x= -5
x-1= 9 x- 1= -9
x= 10 x= -8
x-1=18 x- 1= -18
x= 19 x= -17
x∈{-17;-8;-5;-2;-1;0;2;3;4;7;10;19.}
f) F={x∈ZI _35_ ∈ Z} g) G={x∈ZI _45_ ∈Z}
2x-1 2x+1
35:(2x- 1) , 2x- 1= y 45:(2x+ 1) , 2x+ 1= y
35:y , y∈{+/-1;+/- 5;+/-7; +/- 35} 45:y y∈{+/-1;+/- 5;+/-9;+/-45}
2x- 1= 1 2x- 1= -1 2x+ 1= 1 2x+ 1= -1
x= 1 x=0 x= 0 x= -1
2x- 1= 5 2x- 1= -5 2x+ 1= 5 2x+ 1= -5
x= 3 x=-2 x= 2 x= -3
2x- 1= 7 2x- 1= -7 2x+ 1= 9 2x+ 1= -9
x= 4 x=-3 x= 4 x= -5
2x- 1= 35 2x- 1= -35 2x+ 1= 45 2x+ 1= -45
x= 18 x=-17 x= 22 x= -23
x∈ {-17;-3;-2;0;1;3;4;18.} x∈{-23; -5;-3;-1;0;2;4;22
F={x∈ZI _35_ ∈ Z} g) G={x∈ZI _45_ ∈Z}
2x-1 2x+1
35:(2x- 1) , 2x- 1= y 45:(2x+ 1) , 2x+ 1= y
35:y , y∈{+/-1;+/- 5;+/-7; +/- 35} 45:y y∈{+/-1;+/- 5;+/-9;+/-45}
2x- 1= 1 2x- 1= -1 2x+ 1= 1 2x+ 1= -1
x= 1 x=0 x= 0 x= -1
2x- 1= 5 2x- 1= -5 2x+ 1= 5 2x+ 1= -5
x= 3 x=-2 x= 2 x= -3
2x- 1= 7 2x- 1= -7 2x+ 1= 9 2x+ 1= -9
x= 4 x=-3 x= 4 x= -5
2x- 1= 35 2x- 1= -35 2x+ 1= 45 2x+ 1= -45
x= 18 x=-17 x= 22 x= -23
x∈ {-17;-3;-2;0;1;3;4;18.} x∈{-23; -5;-3;-1;0;2;4;22
i) I={x∈ZI _-25_ ∈ Z} j) J={x∈ZI _30_ ∈Z}
x-1 x-4
-25:(x- 1) , x- 1= y 30:(x- 4) , x- 4= y
-25:y , y∈{+/-1;+/- 5;+/- 25} 30:y, y∈{+/-1;+/- 2;+/-3;+/-5;+/-6;+/-10;+/-15;+/-30.}
x- 1= 1 x- 1= -1 x- 4= 1 x- 4= -1
x= 2 x=0 x= 5 x= 3
x- 1= 5 x- 1= -5 x- 4= 2 x- 4= -2
x= 6 x=- 4 x= 6 x= 2
x- 1= 25 x- 1= -25 x- 4= 3 x- 4= -3
x= 26 x=- 24 x= 7 x= 1
x∈ {-24;-4;0;2;6;26.} x- 4= 5 x- 4= -5
x= 9 x= -1
x- 4= 6 x- 4= -6
x= 10 x= -2
x- 4= 10 x- 4= -10
x= 14 x= - 6
x- 4= 15 x- 4= -15
x= 19 x= -11
x- 4= 30 x- 4= -30
x= 34 x= -26
x∈{-26;-11;-6;-2;-1;1;2;3;5;6;7;9;10;14;19;34.}
Utilizator anonim:
Mai am, dar am simţit să mă aerisesc. Punctele b şi h nu le fac că sunt neclare.
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