Question

Imi trebuie doar A7 si de la A8 subpunctele f) si h).

Answer 1

A8.

[x]+[x]+1+[x]+2 = x+5/2;

3[x] = x+5/2 -3;

3[x] = x - 1/2;

[x] = 2x-1/6

Notez [x] = n, n apartine Z;

n = 2x-1/6

6n = 2x-1

2x = 6n+1

x = 6n+1/2

[x] = 6n+1/2

Folosind poprietatea [x] <= x < [x] + 1 =>

6n+1/2 <= n < 6n+1/2 +1;

6n+1 <= 2n < 6n+3

1 <= -4n < 3

3 < 4n <= 1

3/4 < n <= 1/4

Dar n apatine Z => n = 0 =>

x = 6*0+1/2 =>

x = 1/2 =>

S = {1/2}.