Question

Sa se rezolve ecuatiile :
[x]=2-x
[x+1]=-4
[x]+[x+1]+[x+2]=x+ 5/2

Answer 1

a)
[x]=2-x <=> x=2-[x] apartine Z. => x apartine Z.

Deci [x]=2-x <=> x=2-x <=> 2x=2 <=> x=1.

b)
[x+1]=-4 <=> [x]+1=-4 <=> [x]=-5 <=> x apartine [-5,-4)

c)
[x]+[x+1]+[x+2]=x+5/2 <=> 3[x]+3=x+5/2 <=> 3[x]=x-1/2 <=> 3[x]=[x]+{x}-1/2 <=> {x}=2[x]+1/2. => {x}=1/2 si [x]=0 deci x=[x]+{x}=0+1/2=1/2.