SOLUTION: If a^x=bc;b^y=ca;c^z=ab then prove x/(x+1) + y/(y+1) + z/(z+1) =2

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Question 1072286: If a^x=bc;b^y=ca;c^z=ab then prove x/(x+1) + y/(y+1) + z/(z+1) =2
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
a%5Ex%22%22=%22%22bc;b%5Ey%22%22=%22%22ca;c%5Ez%22%22=%22%22ab then prove x%2F%28x%2B1%29+%2B+y%2F%28y%2B1%29+%2B+z%2F%28z%2B1%29%22%22=%22%222

To avoid doing essentially the same thing three times, 
I'll just do it once with the letters p,q,r,s and use it as
a formula for each of the fractions:

p%5Eq%22%22=%22%22r%2As
log%28%28p%5Eq%29%29%22%22=%22%22log%28%28r%2As%29%29
q%2Alog%28%28p%29%29%22%22=%22%22log%28%28r%29%29%2Blog%28%28s%29%29
q%22%22=%22%22%28log%28%28r%29%29%2Blog%28%28s%29%29%29%2F%28log%28%28p%29%29%29

Therefore,

%22%22=%22%22

and therefore, using the above as a formula,

x%2F%28x%2B1%29+%2B+y%2F%28y%2B1%29+%2B+z%2F%28z%2B1%29%22%22=%22%22

%22%22=%22%22%22%22=%22%22%22%22=%22%222

Edwin