Question

Se dau doua mulțimi, aflați elementele lor. (cu radicali) și A U B.​

Answer 1

Explicație pas cu pas:

V45/(2x-3)€N

Trebuie indeplinite 2 conditii:

1. 45/(2x-3) sa fie nr natural (de la asta pornim)

2. 45/(2x-3)-p.p

45/(2x-3)€N <=>2x-3>0

Deci trebuie sa cautam 2x-3€D45 in multimea nr. naturale

2x-3€{1,3,5,9,15,45} =>

2x€{4,6,8,12,18,48} =>

x€{2,3,4,6,9,24}

45/(2x-3)-p.p

Sa vedem pt ce valori gasite nr. este p.p

x=2=>45/1=45 fals

x=3=>45/3=15(fals)

x=4=>45/5=9 (adevarat)

x=6=>45/9=5 (fals)

x=9=>45/15=3(fals)

x=24=>45/45=1 (adevarat)

Deci A={4,24}

³V(3x+4)/(x-2)€Z <=>

(3x+4)/(x-2)€Z si (3x+4)/(x-2) -cub perfect( c.p)

(3x+4)/(x-2)€Z <=>

x-2|3x+4

x-2|x-2=>x-2|3(x-2)=>x-2|3x-6

Le scadem:

x-2|3x+4-3x+6=>x-2|10 => x-2€D10 in Z =>

x-2€{1,2,5,10,-1,-2,-5,-10} =>

x€{3,4,7,12,1,0,-3,-8}

x=3=>(3x+4)/(x-2)=13/1=13 (fals)

x=4=>16/2=8=2^3 (adevarat)

x=7=>25/5=5 (fals)

x=12=>40/10=4 (fals)

x=1=>7/(-1)=-7(fals)

x=0=>4/(-2)=-2 (fals)

x=-3=> -5/-5=1=1^3 (adevarat)

x=-8=>-20/-10=2 (fals)

Deci B={4,-3}

A U B={3,4,24}