Question

Determinati multimile
C={x€N|15/x-2€N}
D={x€N|13/2x+3€N}
E={x€N|21/4x-1€N}
F={x€N|x-2/x+1€N}
G={x€N|2x+1/x-1€N}

/ = supra

Answer 1

Explicație pas cu pas:

15/x-2€N <=> x-2€D15 in N =>

x-2€{1,3,5,15} => x€{3,5,7,17}

13/2x+3€N <=> 2x+3€D13 in N => 2x+3€{1,13} =>

2x€{-2,10} => x€{-1,5} => x€{5} solutie

21/4x-1€N <=> 4x-1€D21 in N => 4x-1€{1,3,7,21} =>

4x€{2,4,8,22} => x€{1/2,1,2,11/2} => x€{1,2} solutie

x-2/x+1€N <=> x+1| x-2 dar x+1|x+1 => x+1|x+1-x+2 => x+1|3 => x+1€D3 in N =>x+1€{1,3} => x€{0,2} => x€{2} solutie pentru ca fractia sa fie nr natural

2x+1/x-1€N <=> x-1|2x+1

x-1|2x+1

x-1|x-1=>x-1|2x-2

=> x-1|2x+1-2x+2 => x-1|3 => x-1€D3 in Z => x-1€{-3,-1,1,3} =>

x€{-2,0,2,4} => x€{2,4} solutie pt ca fractia sa fie nr natural