aflati numerele a,b,c stiind ca sunt invers proportionale cu 2 3 si 8 si ca 5a+3b-2c=156

a,b,c invers proportionale cu 2,3,8 asta inseamna ca 2a=3b=8c

2a=3b=8c=k
2a=k=>a=k/2
3b=k=>b=k/3
8c=k=>c=k/8

5a+3b-2c=156 inlocuim a,b,c cu cele de sus si rezulta
5*k/2+3*k/3-2*k/8=156
5*k/2+k-k/4=156
10k+4k-k=156*4
13k=624
k=624:13
k=48

a=k/2=48/2=24
b=k/3=48/3=16
c=k/8=48/8=6

{a,b,c}p.i{2,3,8} deci 2a=3b=8c
3b=2a si 2c=a/2
5a+3b-2c=156
5a+2a-a/2=156
14a/2-a/2=312/2
13a=312 deci a=24
b=2*24/3=16
c=a/4=6