If x>0, y>0, z>0, x y+y z+z x < 1 and if ⁻¹ x+ ⁻¹ y+ ⁻¹ z= , then x+y+z equals to

Step-by-step solution

aligned & Given, ⁻¹ x+ ⁻¹ y+ ⁻¹ z= & ⁻¹ ( x+y+z-x y z 1-x y-y z-z x )= & x+y+z-x y z 1-x y-y z-z x = =0 & x+y+z=x y z aligned