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If a,b,c are positive real numbers such that a+b-c/c =a-b+c/b =-a+b+c/a find the value of (a+b)(b+c)(c+a)/ABC

If a,b,c are positive real numbers such that a+b-c/c =a-b+c/b =-a+b+c/a find the value of (a+b)(b+c)(c+a)/ABC
 

Grade:8

3 Answers

Arun
25763 Points
one year ago
Assuming that (a+b+c) is not equal to zero.
Given that,
a+b-c/c=a-b+c/b=-a+b+c/a= **sum of numerators/sum of denominators=1**(A property of ratios)
Therefore,
a+b=2c
a+c=2b
b+c=2a
Therefore,
(a+b)(b+c)(c+a)/abc=2c.2a.2b/abc=8
 
Vikas TU
14149 Points
one year ago
Yashraj
893 Points
one year ago

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