Question

afla numerele naturale xsi y verifica egalitatea 2xy-3x-15=0

Answer 1

2xy-3y-15=0
2xy-3y=15
y(2x-3)=15

x,y € N
=> y(2x-3) € D15={1,3,5,15}

I:y=1=> 2x-3=15 => x=9
II:y=15 => 2x-3=1 => x=2
III:y=3 => 2x-3=5 => x=4
IV:y=5 => 2x-3=3 => x=3

=> (x,y) € {(9,1),(2,15),(4,3),(3,5)}

Answer 2

2xy - 3x -15 = 0
2xy - 3x =15, dam factor comun pe x  ⇒x(2y - 3)=15

x, y ∈ N
⇒ x(2y-3) ∈ D15={1,3,5,15}

daca x = 1⇒1(2y-3)=15⇒2y-3=15⇒2y=15+3⇒2y=18⇒y = 9

daca x = 3⇒3(2y-3)=15⇒6y - 9 = 15⇒6y = 15 + 9⇒6y = 24⇒y = 4

daca x = 5 ⇒5(2y-3)=15⇒10y-15=15⇒10y = 30⇒y = 3

daca x = 15⇒ 15(2y-3)=15⇒30y-45=15⇒30y=60⇒y = 2
deci perechile sunt:
 
(1, 9),  (3, 4),  (5, 3)  si  (15, 2)