Question 96
Find all pairs $(\alpha, \beta)$ of positive real numbers with the following properties:
a. For all positive real numbers $x, y, z, w$,
$$
x + y^{2} + z^{3} + w^{6} \geq \alpha (x y z w)^{\beta}
$$
b. There exists a quadruple $(x, y, z, w)$ of positive real numbers such that equality holds in (a).
a. For all positive real numbers $x, y, z, w$,
$$
x + y^{2} + z^{3} + w^{6} \geq \alpha (x y z w)^{\beta}
$$
b. There exists a quadruple $(x, y, z, w)$ of positive real numbers such that equality holds in (a).