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
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Step-by-step explanation:
a+b-c/c =a-b+c/b
b(a+b-c)=c(a-b+c)
ab+b^2-bc=ac-bc+c^2
ab-ac+b^2-c^2=0
a(b-c)+(b+c)(b-c)=0
(b-c)(a+b+c)=0
=> b-c=0
=> b=c
Similarly c=a
therefore a=b=c
(a+b)(b+c)(c+a)/abc=(a+a)(b+b)(c+c)/abc
2a.2b.2c/abc =8abc/abc
=8
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