Question

determina numerele naturale X daca: a)x|(x+3) b)(2x)|(x+5 ) c)(x+2)|(2x+1)
d) (3x+1)|(2x+5)

Answer 1

x divide pe x+3..vom lucra in N  e ma  scurt decat in Z

(x+3)/x ∈N...1+3/x∈N...3/x∈N x∈D3N={1;3}

b)(x+5)/2x ∈N (2x+10)/2x∈N...1+10/2x∈N....5/x∈N...x∈D5N={1;5}

c)(x+2)/(2x+1)∈N...(4x+4)/(2x+1)∈M...(4x+2+2)/(2x+1)∈N..

...2+2/(2x+1)∈N...2x+1∈D2N={1;2}...2x∈{0;1} , x∈{0;1/2}∩N={0}

d) e mai lung..il faci dupa modelul de la c)

gen...(6x+2)/(2x+5)∈N...(6x+15-13)/(2x+5)∈N...3-13/(2x+5)∈N

2x+5∈D13N...2x+5=1...x=-2∉N si 2x+5=13...x=4 si 3-13/13=3-1=2∈N

x∈{4}