Question 984771: if x = y+z, y = z+x, z = x+y, then what is the value of (1/(x+1)) + (1/(y+1)) + (1/(z+1))?
How to solve this?
Answer by ikleyn(52784)   (Show Source):
You can put this solution on YOUR website!
If x = y+z, y = z+x, z = x+y, then what is the value of  +  +  ?
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You have the system of three linear equations with three unknowns
 .
Add all three equations. You will get
-x - y - z = 0, or
x + y + z = 0. (*)
Now, add the last equation and the first one of the system. You will get
2x = 0, and, hence, x = 0.
Next, add the equation (*) and the second equation of the system. You will get
2y = 0, and, hence, y = 0.
Finally, add the equation (*) and the third equation of the system. You will get
2z = 0, and, hence, z = 0.
Thus your system has a unique solution x = y = z = 0.
Hence, the expression under the question is
+ + = 3.
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