Question

Cine știe sa le rezolve??

Answer 1

7.
2x+1 divide pe5x+13
2x+1 divide pe 10x+26
(10x+5+21)/(2x+1) ∈N
5+21/(2x+1)∈N
 2x+1 divide pe 21
2x+1∈D21={1;3;7;21}
2x+1=1 x=0∉N*
2x+1=3  x=1∈N*
2x+1=7  x=3∈N*
2x+1=21  x=10∈N*
deci A= {1;3;10}

B

2x-1∈D15= {1;3;5;15}
2x-1=1 x=0∈N
2x-1=3 x=2∈N
2x-1=5  x=3∈N
2x-1=15 x=8
x= {0;2;3;8}

A∩B=  {1;3;10}∩ {0;2;3;8}={3}



8.
2x+1 divide pe 5x+19
2x+1 divide pe 10x+38
(10x+38)/(2x+1)∈N
(10x+2 +36)/(2x+1)∈N
5+36/(2x+1)∈N
 36/(2x+1)∈N

2x+1∈D36= {1;2;3;4;6;9;12;18;36}
2x+1=1 x=0∈N
2x+1=2 x=1/2∉N
2x+1=3 x=1∈N
2x+1=4 x=3/2∉N
2x+1=6 x=5/2∉N
2x+1=9 x=4∈N
2x+1=12 x=11/2∉N
2x+1=18 x=17/2∉N
2x+1=36  x=35/2∉N

A={0;1;4} cum A are 3 elemente, card A=3