Solve $b_1 e^{-a_1x^2}-b_2 e^{-a_2x^2}-b_3 e^{-a_3x^2}=0, \forall x$

Question

Suppose, \begin{align*} b_1 e^{-a_1x^2}-b_2 e^{-a_2x^2}-b_3 e^{-a_3x^2}=0, \forall x \end{align*} Assume $a_1,a_2,a_3, b_1,b_2, b_3>0$

What are the possible values of $a_1,a_2,a_3, b_1,b_2, b_3>0$ that satisfy this equation?

One solution is: \begin{align*} b_1=b_2+b_3\\ a_1=a_2=a_3 \end{align*}

Is this a unique solution? Or is there other solutions?