Question

Aflati numerele x si y pentru care (x-1)(y-1)=6

Answer 1

(x-1)(y-1) = 6 =>
Cazul 1:
(x-1)(y-1) = (-1)*(-6) = 6 => x-1 = -1 si y-1 = -6 => x=0 si y= -5
S1 = {(0, -5)}
Cazul 2:
(x-1)(y-1) = (-6)*(-1) => x-1 = -6 si y-1 = -1 => x=-5 si y=0
S2 = {(-5; 0) }
Cazul 3:
(x-1)(y-1) = (-2)*(-3) = 6 => x-1=-2 si y-1= -3 => x=-1 si y=-2
S3= {( -1; -2) }
Cazul 4:
(x-1)(y-1) = (-3)*(-2) = 6 => x-1=-3 si y-1=-2 => x=-2 si y=-1
S4 = {(-2; -1)}
Cazul 5:
(x-1)(y-1)=1*6 = 6 => x-1=1 si y-1 = 6 => x= 2 si y = 7
S5 = {(2; 7)}
Cazul 6:
(x-1)(y-1) = 6*1 = 6 => x-1=6 si y-1 = 1 => x=7 si y= 2
S6 = {(7;2)}
Cazul 7:
(x-1)(y-1) = 2*3 => x-1 = 2 si y-1 = 3 => x=3 si y= 4
S7 = {( 3;4)}
Cazul 8:
(x-1)(y-1) = 3*2 => x-1=3 si y-1 =2 => x=4 si y = 3
S8 = {(4;3)}

S final = {( 0; -5); (-5;0) ; (-1; -2) ; (-2; -1) ; (2; 7) ; (7;2 ) ; (3; 4) ; (4; 3) }