Let X be a proper smooth variety having an affine open subset defined by the normic equation $N_{k(\surd a,\surd b)/k}\left(x\right)=Q(t₁,...,tₘ)²$ over a number field k. We prove that: (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of X; (2) the analogue for rational points is also valid assuming Schinzel’s hypothesis.