Question

[(3x+5)/4]=3x

x=? (apropo, parantezele patrate inseamna parte intreaga)

Answer 1

$\Big[ \frac{3x+5}{4} \Big]=3x \Rightarrow 3x \in Z. \\ \\ Notez~3x=k \in Z \Rightarrow x= \frac{k}{3}.~Inlocuind~in~ecuatia~initiala,~obtinem: \\ \\ \Big[ \frac{k+5}{4} \Big]=k \Rightarrow \frac{k+5}{4}-1\ \textless \ k \leq \frac{k+5}{4} \Leftrightarrow k+1\ \textless \ 4k \leq k+5 \Leftrightarrow \\ \\ \Leftrightarrow 1\ \textless \ 3k \leq 5 \Leftrightarrow \frac{1}{3}\ \textless \ k \leq \frac{5}{3},~dar~k \in Z \Rightarrow k=1 \Rightarrow \boxed{x= \frac{1}{3} } ,~care~ \\ \\ verifica~relatia~din~enunt.$