Given that ad ≠ BC, we prove (A & # 178; + B & # 178;) (C & # 178; + D & # 178;) > AC + BD & # 178;

Given that ad ≠ BC, we prove (A & # 178; + B & # 178;) (C & # 178; + D & # 178;) > AC + BD & # 178;

This is Cauchy inequality
(a^2+b^2)(c^2+d^2)
=a^2·c^2 +b^2·d^2+a^2·d^2+b^2·c^2
=a^2·c^2 +2abcd+b^2·d^2+a^2·d^2－2abcd+b^2·c^2
=(ac+bd)^2+(ad－bc)^2
>(ac+bd)^2

Elden Ring Premiere

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