Question

Wiadomo,że a+b+c=7 i 1/(a+b) + 1/(b+c) + 1/(a+c)= 7/10 . Wyznacz a/(b+c) + b/(c+a) + c/(a+b).

Answer 1

A + b + c = 7
1/(a + b) + 1/(b + c) + 1/(a + c) = 7/10

ponieważ a + b + c = 7, więc a + b + c ≠ 0, więc można obie strony drugiego równania przez a + b + c pomnożyć:

(a + b + c)[1/(a + b) + 1/(b + c) + 1/(a + c)] = 7(a + b + c)/10
(a + b + c)/(a + b) + (a + b + c)/(b + c) + (a + b + c)/(a + c)] = 7*7/10
1 + c/(a + b) + 1 + a/(b + c) + 1 + b/(a + c) = 49/10
c/(a + b) + a/(b + c) + b/(a + c) = 49/10 - 3 = 19/10

jak masz pytania to pisz na pw