Question

Exista a ∈ R astfel incat [(10a-5)/2]=a+1

(Parte intreaga)
Ajutooor!!1

Answer 1

Presupunem ca   [(10a-5)/2]=a+1  

=>  a+1∈Z => a∈Z

a+1<(10a-5)/2<a+1+1

a+1<(10a-5)/2<a+2

a+1<(10a-5)/2     •2

2a+2<10a-5 =>  8a>7

a>7/8  

(10a-5)/2<a+2      •2

10a-5<2a+4

8a<9 => a<9/8  

Din: a>7/8; a<9/8 si a∈Z =>  a=1

=>  [(10a-5)/2]=a+1   pentru a=1