Let a, B, x, y ∈ R and satisfy A2 + B2 = m, X2 + y2 = n, the maximum value of AX + by is ⊙___ .
From Cauchy inequality, we can know that (A2 + B2) (x2 + Y2) ≥ (AX + by) 2, that is, 1 ≥ (AX + by) 2, ax + by ≤ Mn, so the answer is: Mn
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