Question

Determinati numerele a,b,c invers proportionale cu numerele 1,5 ; 2,4 si 3,stiind ca 4a-6b+c=6.

Va rog repede!!!!(:

Answer 1

{a,b,c} i.p{1,5;2,4; 3} => a× 1,5=b×2,4 = c×3=k
Transformam nr. zecimale 1,5 si 2,4 in fractii si avem.
a× 3/2= b×12/5 = 3c=k
3a/2= 12b/5=3c=k

3a/2=k=> 3a= 2k=> a = 2k/3
12b/5=k=> 12b= 5k=> b= 5k/ 12
3c=k=> c= k/3

Si inlocuim in relatia data.
4a-6b+c=6
4× 2k/3 -6× 5K/12 + k/3 =6
Se simplifica 6cu 12 si ramane.
8k/3 - 5k/2 + k/3= 6
Aducem la acelasi numitor care este 6 si avem.
16k/6 - 15k/6+ 2k/6=6
3k/6 =6 => 3k= 6×6 => 3k= 36 => k= 36:3 => k= 12

a= 2k/3=> a = 2×12/3 => a= 24/3 => a=8
b= 5k/12 => b= 5×12/12 => b =60/12=>b= 5
c= k/3 => c= 12/3 => c= 4

Sper ca te.am ajutat!