Question

if a,b,c are positive real numbers such that (a+b-c)/c=(a-b+c)/b=(b+c-a)/a =N , then the value of {(a+b)(b+c)(c+a)}/abc is​

Answer 1

Assuming that (a+b+c) is not equal to zero.

$\textbf{Given that,}$

a+b-c/c=a-b+c/b=-a+b+c/a= sum of numerators/sum of denominators=1(A property of ratios)

$\textbf{Therefore,}$

a+b=2c

a+c=2b

b+c=2a

$\textbf{Therefore,}$,

(a+b)(b+c)(c+a)/abc=2c.2a.2b/abc=8