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Inequalities: Rearrangement: sorted same order max sum products — for math and math max dot?

AM-GM, quadratic inequalities.

Try the problem

Rearrangement: sorted same order max sum products — for (1,2)(1,2) and (3,4)(3,4) max dot?

Hint and answer

Concept to use

AM-GM two variables.

Hint

2⋅4+1⋅32\cdot4+1\cdot3.

Answer

11

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