It is proved that for any a, B, C, D ∈ R, there is an inequality (AC + BD) ≤ (a + b) (c + D),

It is proved that for any a, B, C, D ∈ R, there is an inequality (AC + BD) ≤ (a + b) (c + D),

(a + b) (c + D) - (AC + BD) = AD + bc-2abcd = (AD BC) ≥ 0
Thank you!