Question

1.determinati numerele a si b, stiin ca invers proportionale cu 1/6 si1/3 si diferenta lor este 30

2. determinati numerele a si b, stiin ca invers proportionale cu 1/5 , 1/4 si 1 si a-2c=0,3

va rog ajutati-ma

Answer 1

{a,b} i.p{1/6, 1/3}
a-b=30
a·1/6=b·1/3=k
a/6=k⇒a=6k
b/3=k⇒b=3k
a-b=30⇒
6k-3k=30
3k=30
k=30/3
k=10
a=6k=6·10⇒a=60
b=3k=3·10⇒b=30


{a,b,c} i.p.{1/5, 1/4, 1}
a·1/5=b·1/4=c·1=k
a/5=k⇒a=5k
b/4=k⇒b=4k
c=k
a-2c=0,3
5k-2k=3/10
3k=2/10
k=2/10·3
k=2/30
a=5k=5·2/30=10/30⇒a=1/3
b=4·2/30⇒b=4/15
c=2/30⇒simplificam⇒c=1/15