Question

abc-triunghi, ab=3cm ac=x+1,bc=x+2. Aflati x-nr. natural

Answer 1

terxt corectat
 
ABC-triunghi, AB=3cm AC=x+1,BC=x+2. Aflati x-nr. natural

aplicam inegalitatea triunghiului pt latura AB
(x+2)-(x+1)<3<x+2+x+1
1<3<2x+3
3>1 oricare x
 2x+3>3 pt x>0 cum xe numar natural si x>0 ⇒x∈N*

verificam siptrcelelate laturi
pt latura BC
|3-(x+1)|<x+2<x+1+3
 parte a doua e adevarta ∀x
ramane x+2>|2-x|
x+2>|x-2| adevarat∀x≥2
si verificam si pt x=1
3>|-1|=1 adevarta
deci solutia x∈N* ramane


verificam, si pt laturaAC
|x+2-3|<x+1<x+2+3
 |x-1|<x+1<x+5
cum x≥1, putem scrie
x-1<x+1<x+5 adevarat ∀x∈N*

deci solutie final x∈N*
 in atasament  ai cateva verificari pt x=1 (minim) x=6 si x=11