Consider three real numbers x, y, and z that satisfy this system of equations:
- x+y+z=5
- 1/(x+y) + 1/(y+z) +1/(z+x) =4/5
Find the value of x/(y+z) + y/(z+x)+ z/(x+y).
Start with the Unknown to be found, call it U:
x/(y+z) + y/(z+x)+ z/(x+y) = U
x/(5-x) + y/(5-y)+ z/(5-z) = U
1/(5-x) + 1/(5-y) + 1/(5-z) = 4/5
(x + y + z)*(1/(5-x) + 1/(5-y) + 1/(5-z)) = 4
x/(5-x) + y/(5-y)+ z/(5-z) + (y+z)/(5-x) + (x+z)/(5-y)+ (x+y)/(5-z) = 4
U + (y+z)/(5-x) + (x+z)/(5-y)+ (x+y)/(5-z) = 4
U + (y+z)/(y+z) + (x+z)/(x+z)+ (x+y)/(x+y) = 4
U + 3 = 4
U = 1
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Posted by Larry
on 2023-10-09 09:35:13 |
No Subject
