Question

Fie numerele rationale nenule a, b, c si x astfel incat 2(a+b)=6(b+c)=8(c+a)=x(a+b+c). Determinati x

Answer 1

2(a+b)=6(b+c)|:2=>+a+b=3b+3c=>4b=a-3c=>b=(a-3c)/4

2(a+b)=8(c+a)|:2=>a+b=4c+4a<=>a+(a-3c)/4=4c+4a |*4=>5a-3c=4c-4a=>9a=7c=>a=7c/9

b=(a-3c)/4=(7c/9-3c)/4=c/9/4=c/36

2(a+b)=x(a+b+c)<=>2(7c/9+c/36)=x(7c/9+c/36+c)<=>58c/36=65c/36 x|:c/36=>58=65x=>x=58/65

x=58/65

Sper sa nu fi gresit la calcule