Minimize the Function F(x) = X + Y, Subject to the Constraint

Short Answer

Minimize the function f(x) = x + y, subject to the constraint xy = 100, x > 0, y > 0. Use the method of Lagrange multipliers.
Enter your answer exactly as just (a, b), c where (a, b) gives the minimum and c is the Lagrange multiplier as a reduced fraction of form $\frac { d } { e }$ (no words or labels).