Question

Determinati elementele multimilor A={x€N| (x-1)|(2x+3)} B={x€N| (2x+3)|(3x+7)}

Answer 1

Explicație pas cu pas:

x-1|2x+3

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

=> x-1|2x+3-2x+3=>x-1|5 => x-1€D5 in Z =>

x-1€{-5,-1,1,5} =>

x€{-4,0,2,6} => A={0,2,6} (ne cere x€N)

2x+3|3x+7=>2x+3|6x+14

2x+3|2x+3=>2x+3|6x+9

=>2x+3|6x+14-6x-9=>2x+3|5 => 2x+3€D5 inZ =>

2x+3€{-5,-1,1,5} =>

2x€{-8,-4,-2,2} => x€{-4,-2,-1,2} => B={2}

la 2x+3|5 era suficient sa slune ca apartine divizorilor naturali pentru ca daca x€N si 2x+3€N deci este suficinet sa cautam 2x+3€N