Question

Care este partea intreaga a lui [3x] = X pe 2​

Answer 1

Răspuns:

intrebare ....mai bine nu o puneai si ziceai "sa se rezolve ecuatia"

raspuns x=0

Explicație pas cu pas:

[3x]=x/2

deci x intreg si par, pt ca x/2 ∈Z

pornim de la

[x]≤x<[x]+1

x/2≤x<x/2+1

x≤2x<x+2

0≤x<2

x∈[0,2)

dar x intreg si par

solutie unica x=0

Answer 2

$\it [3x]=\dfrac{x}{2}\\ \\ Fie\ k\in\mathbb{Z},\ \ \dfrac{x}{2}=k \Rightarrow x=2k\ \ \ \ \ (1)\\ \\ Ecua\c{\it t}ia\ devine:\\ \\ \big[ 6k\big]=k \Rightarrow -k\leq6k<k+1 \Rightarrow \begin{cases} \it -k\leq6k|_{+k} \Rightarrow 0\leq7k \Rightarrow 0\leq k\\ \\ \it6k<k+1|_{-k} \Rightarrow 5k<1|_{:5} \Rightarrow k<\dfrac{1}{5}\end{cases} \Rightarrow \\ \\ \\ \Rightarrow 0\leq k<\dfrac{1}{5}\ \stackrel{k\in\mathbb{Z}}{\Longrightarrow}\ k=0\ \ \ \ \ (2)$

$\it (1),\ (2) \Rightarrow x=2\cdot0 \Rightarrow x=0$