If ⁻¹ x+ ⁻¹ y+ ⁻¹ z= 2 , x, y, z>0, x y < 1, then the value of x y+y z+z x=

Step-by-step solution

⁻¹ x+ ⁻¹ y+ ⁻¹ z= 2 ( ⁻¹ x+ ⁻¹ y )= ( 2 - ⁻¹ z ) ⁻¹ ( x+y 1-x y )= ⁻¹ z= ⁻¹ ( 1 z ) x+y 1-x y = 1 z x z+y z=1-x y x y+y z+z x=1