A question on harmonic two-forms

Question

Let $(M^4,g)$ be a closed Riemannian four-manifold with $b_2^+>0$ and $b_2^->0$, is it possible to find two harmonic two-forms $\alpha\in H^2_+(M)$ and $\beta\in H^2_-(M)$, such that \begin{equation*} |\alpha(x)|^2=|\beta(x)|^2\quad\text{for all } x\in M ? \end{equation*} Thank you.