Question

[x+1/3]+[x+1/5]=1 va roog

Answer 1

Răspuns:

x∈[2/3; 4/5)

Explicație pas cu pas:

[x]∈Z

posibil

doar 0+1 sau 1+0 ***

cum x+1/5<x+1/3

convine doar =[x+1/3]=1...x∈[2/3, 5/3)

SI

[x+1/5]=0....x∈[0,4/5)

[2/3, 5/3)∩[0,4/5)=[10/15, 25/15)∩[0, 12/15)=[10/15; 12/15)=[2/3; 4/5)

GREA! (pt mine...:) )

***P.S .

nu am verificat si

1=2+(-1)

[x+1/3]=2...x∈[2/3; 8/3)

[x+1/5]=-1...x∈[-6/5;-1/5) cu intersectie  vida

analog si urmatoarele perechi posibile

deci ramane un singur interval