Răspuns:
Explicație pas cu pas:
(a+b+c)/3= 4+8 radical 2
a+b+c= 3 ori (4+8 radical 2)
a+b+c=12 + 24 radical 2
a) a= 3 + radical 32
Radical 32=4 radical 2
Din astea doua=> a= 3 + 4 radical2
b= 5+ radical 72
Radical 72= 6 radical 2
Dibastea doua => b= 5+6 radical 2
Acum avem:
a+b+c= 12+24 radical 2
Si: a= 3+4 radical 2
b= 5+6 radical 2
Inlocuim mai sus si vom avea
a+b+c=12+24 radical 2
3+ 4 radical 2+ 5+6radical 2+c= 12+24 radical 2
8+ 10 radical 2+c= 12+ 24 radical 2
C= 12+24 radical 2 - 8-10 radical 2
C= 4 +14 radical 2
b) a+b+c= 12+24 radical 2
2a=3b=6c
2a=3b=> a= 3b/2
Inlocium mai sus si vom avea
3b/2+ b+c= 12+ 24 radical 2
(3b+2b)/2+c= 12+24 radical 2
5b/2+c= 12+24 radical 2
3b=6c=> c= 3b/6
Inlocium mai sus si vom avea
5b/2+ 3b/6= 12+ 24 radical 2
(15b+3b)/6= 12+24 radical 2
18b/6= 12+ 24 radical 2
3b= 12+ 24 radical 2
b= (12+ 24 radical 2)/3
b= 3 ori (4+ 8 radical 2)/3
b= 4+ 8 radical 2
c= 3b/6=> c= [3 ori (4+ 8radical 2)/6]
c= (4+ 8 radical 2)/2 = 2 ori (2+ 4 radical 2)/2= 2+ 4 radical 2
a= 3b/2=> a= [3 ori (4+ 8 radical 2)/2]
a= (12+ 24 radical 2)/2= 2 ori ( 6+ 12 radical 2)/2= 6+12 radical 2
Pentru punctul b) Mai este o metoda de rezolvare cu k. Iata metoda
2a+3b+6c=k
2a=k=> a=k/2
3b= k=> b= k/3
6c= k=> c= k/6
a+ b+c=12+ 24 radical 2
K/2+ k/3+k/6= 12+24 radical 2
(3k+ 2k+k)/6= 12+ 24 radical 2
6k/6= 12+24 radical 2
K= 12+24 radical 2
a= k/2=> a= (12+ 24 radical 2)/2= 2 ori (6+ 12radical 2)/2= 6+ 12 radical 2
b= k/3=> b= 12+24 radical 2/3= 3 ori (4+ 8 radical 2)/3= 4+ 8 radical 2
c= k/6=> c=( 12+24 radical 2)/6= 6 ori (2+ 4 radical 2)/6= 2+ 4 radical 2
