Question

Sa se afle numerele x,y,z eQ stiind ca
sunt direct proportionale cu 3,4,5 si 1/x +
1/y +1/z=47/80

Va rog!​

Answer 1

Răspuns:

{x, y, z} d.p. {3, 4, 5} => x/3=y/4=z/5=k => x=3k

y=4k

z=5k

1/x+1/y+1/z=47/80

1/3k+1/4k+1/5k=47/80 |×60

20/60k+15/60k+12/60k=47/80

47/60k=47/80

60k=80 => k=80/60=4/3 => x=3×4/3=3

y=4×4/3=16/3

z=5×4/3=20/3