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).
Absolutely nothing wrong with the other solutions, but I'm too lazy to multiply polynomials, so I took this route:
x / (y + z) = (5 - (y+z)) / (y+z) by the first equality which simplifies to
5 /(y+z) - 1.
Ditto for the other two parts of the expression which then becomes:
5(1/(y+z) + 1/(x+z) + 1/(x+y)) - 3
Substituting in the second equality yields
5(4/5) - 3 = 4-3 = 1
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Posted by Paul
on 2023-10-09 11:30:47 |
Like we really need another solution...
