Question

Aflati x,y,z direct proportionale cu 0,25;0,(3);0,5 daca xy+xz+yz=3xyz

Answer 1

0,25=25/100=1/4
0,(3)=3/9=1/3
0,5=5/10=1/2
{x,y,z}dp{1/4, 1/3, 1/2}
x/4=y/3=z/2=k
x=4k
y=3k
z=2k
xy+xz+yz=3xyz
4k·3k+4k·2k+3k·2k=3·4k·3k·2k
12k²+8k²+6k²=72k³
26k²-72k³=0
k²(26-72k)=0
26-72k=0
-72k=-26      inmultim -1
k=26/72=13/34
k=13/34
x=4k=4·13/34=2·13/17=26/17
x=26/17
y=3k=3·13/34=39/34
y=39/34
z=2k=2·13/34=13/17
z=13/17