Question

Numerele rationale pozitive a,b,c sunt direct proportionale cu nr. 2,3 si 4.Stiind ca 6a²+b²-2c²=9,determinati nr.a ,b,c

Answer 1

{a,b,c}dp{2,3,4}
a/2=b/3=c/4=k
a/2=k rezulta a=2k
b/3=k rezulta b=3k
c/4=k rezulta c=4k
inlocuim in relatia 6a²+b²-2c²=9
6·2²k²+3²k²-2·4²k²=9
24k²+9k²-32k²=9
k²=9
k=+/-√9
k1=3
k2=-3

cazul I daca k=3
a=2k=2x3=6
b=9
c=12

cazul II daca k=-3
a=-6
b=-9
c=-12