i need help with the algebra question

[20261211]

If x/(b+c-a)=y/(c+a-b)=z/(a+b-c)
Prove (x+y+z)/(a+b+c)=(x*(y+z)+y*(z+x)+z*(x+y))/(2*(ax+by+cz)

 

[Dr.Peterson]

If x/(b+c-a)=y/(c+a-b)=z/(a+b-c)
Prove (x+y+z)/(a+b+c)=(x*(y+z)+y*(z+x)+z*(x+y))/(2*(ax+by+cz)

I don't know what method you are expected to use; I imagine there is a very elegant approach I haven't learned.

But one way to start is to let x/(b+c-a) = y/(c+a-b) = z/(a+b-c) = k, and then express x, y, and z in terms of a, b, c, and k. You will find that (x+y+z)/(a+b+c) is equal to something very simple. Similarly work out (x*(y+z)+y*(z+x)+z*(x+y))/(2*(ax+by+cz) and see if it equals the same simple expression.

Or, tell us, as we ask you to do, what you have tried and what you have learned, so we can try to find an answer you will understand:

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