Show that there is a constant C > 0 so that for any set A = {a1, . . . , an} of n > 0 distinct real numbers

Question

For any two sets A, B of real numbers denote A + B := {a + b | a ∈ A, b ∈ B} and A × B := {a · b | a ∈ A, b ∈ B}. Show that there is a constant C > 0 so that for any set A = {a1, . . . , an} of n > 0 distinct real numbers at least one of the following inequalities is satisfied

1. |A + A| ≥ C*n^(5/4)
2. |A × A| ≥ C*n^(5/4)

I try To bound |P| = |A + A| · |A × A| from below, using the upper bound on the number of incidences between points P = (A+A)×(A×A) and (n chosee 2) lines of the form `i,j : y = ai(x−aj ). and that the number of such incidences is at least Ω(n^3). but I didnt know how to progress from here ..