If u= ⁻¹ ( x y )+ ⁻¹ ( y x ) , then the value x u x +y u y is

Step-by-step solution

aligned & u= ⁻¹ ( x y )+ ⁻¹ ( y x ) & u x = 1 1- ( x y )^2 1 y + 1 1+ ( y x )^2 (- y x^2 ) aligned = 1 (y^2-x^2 ) - y (x^2+y^2 ) array r u y = 1 1- ( x y )^2 (- x y^2 )+ 1 1+ ( y x )^2 ( 1 x ) =- x y (y^2-x^2 ) + x (x^2+y^2 ) array On adding Eqs. (i) and (ii), we get x u x +y u y =0