Question

1)A={x∈N*/2·x-1≤7}, B={y∈N/ y=2 LA PUTEREA X ,x∈A} si C={z∈N /z=3x-1 ,x ∈A}. Determinati multimile A,B,C si A intersectat cu B , A reunit cu B reunit cu C, B intersectat cu C , (B/C) REUNIT CU (A/C).
2)Daca a ·b=15 si a·c=17 , atunci a(b+c) este..........
3)Scrieti rezolvari complete:
Aflati numerele naturale x;
a) 3 la puterea x +3 la puterea x +1 + 3 la puterea x +2 =117
b)x+2x+3x+....+100x=1000

VA ROG AJUTATIMA!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

Answer 1

1)
2x-1≤7
2x≤7+1
2x≤8
x≤8/2
x≤4
A={1,2,3,4}

y=2^x
y=2, 2², 2³, 2⁴
y=2,4,8,16
B={2,4,8,16}

z=3x-1
x=1,2,3,4
z=2,5,8,11
C={2,5,8,11}
Aintersectat B={2,4}
AUBUC={1,2,3,4,5,8,11,16}
Bintersectat C={2,8}
(B/C)U(A/C)={4,16}U{1,3,4}={1,3,4,16}

2)a(b+c)=ab+ac=15+17=32

3)3^x+3^(x+1)+3^(x+2)=117
3^x+3·3^x+3²·3^x=117
3^x+3·3^x+9·3^x=117
notam 3^x=a
a+3a+9a=117
13a=117
a=117/13
a=9
3^x=9
3^x=3²
x=2