find the value of (a+b)(b+c)(c+a)/abc

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
kavitha
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find the value of (a+b)(b+c)(c+a)/abc

Postby kavitha » Thu Feb 27, 2014 3:42 am

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

nona.m.nona
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Re: find the value of (a+b)(b+c)(c+a)/abc

Postby nona.m.nona » Thu Feb 27, 2014 11:30 pm

kavitha wrote:If a,b,c are positive real numbers said 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)/c = (a - b + c)/b = (-a + b + c)/a = k, then, for instance, (a + b - c)/c = k, so a + b - c = kc, so a + b = c(k + 1). Where might this lead one's investigation?

kavitha
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Re: find the value of (a+b)(b+c)(c+a)/abc

Postby kavitha » Mon Mar 03, 2014 3:29 pm

Thank you.


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