Question

Rezolvati in Z ecuatia
lx-5l+ly-8l=1

Answer 1

|x-5|+|y-8|=1

x si y € Z => x-5 si y-8€Z

|a|≥0

Cazuri:

1. x-5=1 si y-8=0

2. x-5=0 si y-8=1

3. x-5=-1 si y-8=0

4. x-5=0 si y-8=-1

Perechiile sunt: (6, 8) ; (5, 9) ; (4, 8) ; (5, 7)

Answer 2

lx-5l + ly-8l = 1

(1) |x-5| = 1:

{x = 4; x = 6}, {y = 8}

(2) |y-8| = 1:

{x = 5}, {y = 7; y = 9}

⇒ (x, y) = {(4, 8); (6, 8); (5, 7); (5, 9)}