Let x be a real number. [x] denotes the greatest integer function, x denotes the fractional part and (x) denotes the least integer function, then solve the following.
(i) $(x)^2 = [x]^2 + 2x
(ii) $[2x] - 2x = [x + 1]
(iii) $[x^2] + 2[x] = 3x, 0 \le x \le 2
(iv) y=4−[x]2 and $[y] + y = 6
(v) [x]+∣x−2∣≤0 and $-1 \le x \le 3