Question

Determinati numerele a, b, c stiind ca sunt invers proportionale cu 4, 3 si 2 si ca ab+ac+bc = 54

Answer 1

{a,b,c} i.p. {4,3,2}.
a•4=b•3=c•2=k.
a•4=k rezulta a=k/4.
b•3=k rezulta b=k/3
c•2=k rezulta c=k/2.
(k/4•k/3)+(k/4•k/2)+(k/3•k/2)=54
k/12+k/8+k/6=54
ridici la putere si obtii:
2k/24+3k/24+4k/24=54
inmultesti cu 24 ca sa scapi de nimitor si obtii:
2k+3k+4k=54
9k=54
k=54:9
k=6.
a=9/4
b=9/3
c=9/2