Question

Rezolvați în R:
{x}=(x-1)2
{3x}=x/2

Answer 1

{x}=(x-1)/2

C.E.

0≤(x-1)/2<1

0≤x-1<>2

1≤x<3⇒[x]∈{1;2}

{x}=x-[x]

(x-1)/2=x-1⇒(x-1)/2=0⇒x=1 care ∈[1;3) siverifica {1}=0

(x-1)/2=x-2⇒2x-4=x-1....x=3 care nu apartine dom de def...

deci solutie unica x=1

x/2∈[0,1)⇒x∈[0;2)⇒[x]∈{0;1}

{3x}=3x-[3x]

x/2=3x-[3x]

x/2=3x-0

0=5x/2...x=0care apartine [0.2)- si verifica {3*0}=0/2

x/2=3x-1

1=3x-x/2

1=5x/2

x=2/5 care ∈[0,2) si vweerifica {3*2/5}={6/5}=1/5 si (2/5) :2=1/5