For x y 1 , let _x ( x y )+ _y ( y x )=k , then the value of k can never be equal to:

Step-by-step solution

_x ( x y )+ _y ( y x )=k aligned & _x x- _x y+ _y y- _y x=k & 1- _x y+1- 1 _x y =k & Let, _x y=t & 2-t- 1 t =k & 2 t-t^2-1=k t & t^2+(k-2) t+1=0 & For solution, D =b^2-4 a c 0 & (k-2)^2-4 0 (k-2)^2 0 & k-2 2 k-2 0 & k 4 k 0 & k 4 or k 0 aligned Hence, k 1 .