If xy = -6 and x³ + y³ = 19 (x and y are integers), then what is the value of $$\frac{1}{{{x^{ - 1}}}} + \frac{1}{{{y^{ - 1}}}}?$$

Solution (By Examveda Team)

$$\eqalign{ & xy = - 6,\,{x^3} + {y^3} = 19 \cr & {\text{putting }}x = 3,\,y = - 2 \cr & {\text{both condition are satisfied}} \cr & {\text{So, }}\frac{1}{{{x^{ - 1}}}} + \frac{1}{{{y^{ - 1}}}} \cr & = x + y \cr & = 3 - 2 \cr & = 1 \cr} $$