Question

Determinati numerele a,b si c invers proportionale cu numerele 1,5 ; 2,4 si 3 daca 4a-6b+c=6.
(Nu am voie sa folosesc numerele intregi).
Multumesc mult!!! :) :) :) :) :*

Answer 1

{ a, b, c } i.p { 1,5 ; 2,4 ; 3 }
a x 3/2 = b x 12/5 = c x 3 = k
a x 3/2 = k ⇒ a = 2k/3
b x 12/5 = k ⇒ a = 5k/12
c x 3 = k ⇒ c = k/3
4a - 6b + c = 6
4 x 2k/3 - 6 x 5k/2 + k/3 = 6
2)     3)        2)
8k/3 - 5k/2 + k/3 = 6
16k/6 - 15k/6 + 2k/6 = 6
3k/6 = 6
3k = 6 x 6
3k = 36
k = 12
a = 2 x 12 / 3 = 24/3 = 8
b = 5 x 12 / 12 = 5
c = 12/3 = 4