Question

[X]+[x+1]+[x+2]=x+5/2 unde [x] reprezinta partea intreaga a numarului x si x numar real

Answer 1

[x]+[x+1]+[x+2]=x+5/2
[x]+[x]+[x]+1+2=x+5/2
3[x]=x-1/2
x=2x-1/6=a, a apartine lui Z=>X=6a+1/2
[6a+1/2]=a
a(mai mic sau egal decat)6a+1/2<a+1
2a(mai mic sau egal decat)6a+1<2a+2
0(mai mic sau egal decat)4a+1<2
-1(mai mic sau egal decat)4a<1
-1/4mai mic sau egal decat)a<1/4 => a apartine [-1/4;1/4),a apartine lui Z=>a=0=>x=1/2