Question: Prove carefully: a, b, c, d R, if a < b and c > d, then ad + bc > ac + bd. HINTS:

Prove carefully: " a, b, c, d R, if a < b and c > d, then ad + bc > ac + bd.

HINTS: What can you deduce about the sign of (b - a)(d - c), and what do you get when you multiply this out?

You can assume that the usual algebraic rules of inequalities apply, without citing an axiom or theorem.

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