a=xy/x+y , b=yz/y+z ,c=zx/z+x here abc is not equal to zero then what is x?
Answers
Step-by-step explanation:
xy/(x+y) is the same as 1/(1/x+1/y)
so we can rewrite xy/(x+y) = a
as
1/x+1/y = 1/a (1)
also rewrite xz/(x+z) = b
as
1/x+1/z = 1/b (2)
add (1) and (2)
==> 2/x+1/y+1/z = 1/a+1/b
but we also know that 1/z+1/y = 1/c
so 2/x+1/c = 1/a+1/b
so 2/x = 1/a+1/b-1/c = (bc+ac-ab)/abc
so x = 2abc / (bc+ac-ab)
QED
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Step-by-step explanation:
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