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Let a, b, c be real number such that a + b + c = 5 and 1/(b + c) + 1/(c + a) + 1/(a + b) = 6.  Find a/(b + c) + b/(c + a) + c/(a + b).

 Dec 1, 2019
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a + b + c = 5.     (1)

 

Divide (1) by b + c:    a/(b+c) + 1 = 5/(b+c).  (2)

Divide (1) by a + c:    b/(a+c) + 1 = 5/(a+c).   (3)

Divide (1) by a + b:    c/(a+b) + 1 = 5/(a+b).   (4)

 

Add (2), (3) and (4): a/(b+c) + b/(a+c) + c/(a+b) + 3 = 5*6

Hence  a/(b+c) + b/(a+c) + c/(a+b) = 27

 Dec 1, 2019

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