Question

Determinati numerele intregi x si y pentru are:
a)xy=-6
b)(2x+1)y=21
c)(x-4)(y+3)=35

Answer 1

x y = - 6
2 x ( - 3 ) = - 6 sau  - 2 x 3 = - 6
( 2x + 1 ) y = 21
   7 x 3 = 21
2x + 1 = 7  ⇒2x = 7 - 1⇒2x = 6⇒x = 3
 (2x3 + 1)x3 = 21
(x - 4 ) ( y + 3 ) = 35
7 x 5 = 35
x - 4 = 7⇒x = 7 + 4 ⇒x = 11
y + 3 = 5⇒y = 5 - 3⇒y = 2
( 11 - 4 ) ( 2 + 3 ) = 35

Answer 2

a)... x*y=-6=(-1*6)=1*(-6)=-2*3=2*(-3)
   ⇒(x,y)={(-1,6) , (1, -6) , (-2,3) , (2,-3)} ,          (si invers ...)
b)... (2x+1)(y)=21=-1*21=1*(-21)=-3*7=3*(-7)
       (x,y)={-1,21) , (0,-21) , (-2,7) , (1,-7)} ,        (si invers ...)
c)... (x-4)(y+3)=35=-1*(-35)=1*35=-5*(-7)=5*7
        (x,y_={(3,-38) , (5,32) , (-1,-10) , (9,4)}      (si invers ..._