Question

Determinati numerele x,y si z invers proportionale cu 0,4 0,5 si 0,75 stiind ca x+y-3z=3

Answer 1

0,4=4/10=2/5
0,5=5/10=1/2
0,75=75/100=15/20=3/4
x+y+3z=3
{x,y,z}ip{2/5,1/2,3/4}
2x/5=y/2=3z/4=k
2x/5=k rezulta x=5k/2
y/2=k rezulta y=2k
3z/4=k rezulta z=4k/3
5k/2+2k-3·4k/3=3
5k/2+2k-4k=3
5k/2-2k=3
(5k-4k)/2=3
k=3·2
k=6
x=5k/2=(5·6)/2=15
y=2k=2·6=12
z=4k/3=(4·6)/3=8
15+12-3·8=3
27-24=3