SOLUTION: 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?

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(52786)   (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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