cum se rezolva (x+5)×(y-4)= 3×3×2×2:1
Răspunsuri la întrebare
Răspuns:
Explicație pas cu pas:
(x+5)×(y-4)= 3×3×2×2:1 <=>
(x+5)×(y-4)= 36 =>
36 I 3
12 I 3
4 I 2
2 I2
1
36 = 2²·3²
Divizorii intregi ai lui 36 sunt:
± 1 ; ± 2 ; ± 3 ; ± 4 ; ± 6 ; ± 9 ; ± 12 ; ±18 ; ± 36
Avem : (-1 )·(-36) = 36 ; (-2)·(-18) = 36; (-3)·(-12) = 36
(-4)·(-9) = 36 ; (-6)·(-6) = 36 ; (-9)·(-4) = 36 ;
(-12)·(-3) ; (-18)·(-2) ; (-36)·(-1) si toate celelalte inmultiri pozitive
=>
x+5 = -1 => x = -6 ; y-4 = -36 => y = -32
x+5 = 1 => x = -4 ; y-4 = 36 => y = 40
x+5 = -2 => x = -7 ; y-4 = -18 => y = -14
x+5 = 2 => x = -3 ; y-4 = 18 => y = 22
x+5 = -3 => x = -8 ; y-4 = -12 => y = -8
x+5 = 3 => x = -2 ; y-4 = 12 => y = 16
x+5 = -4 => x = -9 ; y-4 = -9 => y = -5
x+5 = 4 => x = -1 ; y-4 = 9 => y = 13
x+5 = -6 => x = -11 ; y-4 = -6 => y = -2
x+5 = 6 => x = 1 ; y-4 = 6 => y = 10
x+5 = -9 => x = -14 ; y-4 = -4 => y = 0
x+5 = 9 => x = 4 ; y-4 = 4 => y = 8
x+5 = -12 => x = -17 ; y-4 = -3 => y = 1
x+5 = 12 => x = 7 ; y-4 = 3 => y = 7
x+5 = -18 => x = -23 ; y-4 = -2 => y = 2
x+5 = 18 => x = 13 ; y-4 = 2 => y = 6
x+5 = -36 => x = -41 ; y-4 = -1 => y = 3
x+5 = 36 => x = 31 ; y-4 = 1 => y = 5
Pentru x,y ∈ N avem :
(x, y) = (1 , 10) ; (4 , 8) ; (7 , 7) ; (13 , 6) ; (31 , 5)