Question

Determinati numerele nenule a, b, c invers proportionale cu 5, 6, 10 stiind ca a la puterea 2 + b la puterea 2 + c la puterea 3 supra abc = 7 supra 9

Answer 1

5a=6b=10c=k
a=k/5
b=k/6
c=k/10
(k^2/25 + k^2/36 + k^2/100) : k^3/300 = 7/9
25=5^2
36=2^2 • 3^2
100=2^2 • 5^2
___________
cmmmc=2^2 • 3^2 • 5^2 = 900
(36k^2 + 25k^2 + 9k^2)/900 • 300/k^3 = 7/9
70k^2/900 • 300/k^3 = 7/9
70/3k = 7/9
21k=630 =>k=30
a=6
b=5
c=3