Răspuns:
a = 1/18 ; b = 1/27 ; c = 1/45
Explicație pas cu pas:
{a ; b ; c} i.p. {2 ; 3 ; 5} <=>
2a = 3b = 5c => a = 3b/2 ; c = 3b/5
1/a + 1/b + 1/c = 90 <=>
(bc+ac+ab)/abc = 90 =>
bc+ac+ab = 90abc
²⁾3b²/5 + 9b²/10 + ⁵⁾3b²/2 = 90·3b/2 · b · 3b/5 =>
(6b²+9b²+15b²)/10 = 810·b³/10 =>
30b² = 810b³ =>
b = 30/810 = 3/81 = 1/27
a = (3/27):2 = 1/18
c = (3/27):5 = 1/45
1/a = 1/(1/18) = 18
1/b = 1/(1/27) = 27
1/c = 1/(1/45) = 45 =>
1/a+1/b+1/c = 18+27+45 = 90
a = 1/18 ; b = 1/27 ; c = 1/45
