Let \( x \) be a real number. \( [x] \) denotes the greatest integer function, \( \{x\} \) denot...

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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) \( (x)^{2}=[x]^{2}+2 x \)
(ii) \( [2 x]-2 x=[x+1] \)
(iii) \( \left[x^{2}\right]+2[x]=3 x, 0 \leq x \leq 2 \)
(iv) \( y=4-[x]^{2} \) and \( [y]+y=6 \)
(v) \( [x]+|x-2| \leq 0 \) and \( -1 \leq x \leq 3 \)
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