Question

Dacă a/b =3/4 ; b/a = d/c=f/e și 2a+3c+4e=72 , calculați 6b+ 9d+12f.

Answer 1

a/b=3/4 => 3b=4a =>
b=4a/3
2a=3b/2
3b/2+3c+4e=72
d/c=f/e
b/a=d/c
b=ac/d
e=af/b
c=ad/b
a=bc/d
b=ad/c
d=bc/a
2(bc/d)+3(ad/b)+4(af/b)=72
2bc/2+(3ab+4af)/b=72
2bc/2+(3ab+3bf)/b=72
2bc/2+[3b(a+f)]/b=72
bc+[3b(a+f)]/(4a/3)=72
(4ac/3)+3b(a+f)•(3/4a)=72
(4ac/3)+[3•3b(a+f)]/4a=72