Question

rezolvați ecuatia :
[x] =( x+1)/2

Answer 1

[x]≤x<[x]+1 |inmultim cu 2
2[x]≤2x<2[x]+2

dar 2[x]=x+1 din ecuatia data
deci
x+1≤2x<x+1+2
sau
x+1≤2x<x+3 | scadem x

1≤x<3
x∈[1;3)
dar 2[x]=x+1

2[x]∈Z, 1∈Z⇒x∈Z
deci x∈{1;3)∩Z={1;2}
dar 2 nu verifica, pt ca (1+2)/2∉Z
deci S={1}