Question

{a,b,c} i.p {2,3,5}
1+1+1=?
a b c
a,b,c=?
dau 5 stele
a adaugat si o poza ca sa se vada mai bine​

Answer 1

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