Let-a-b-c-d-e-1-and-a-b-c-d-e-5-Find-the-maximum-and-minimum-value-of-S-a-b-b-c-c-d-d-e-e-a-

Question Number 61268 by alphaprime last updated on 31/May/19

$${Let}\:{a},{b},{c},{d},{e}\:\geqslant\:−\mathrm{1}\:{and}\:{a}+{b}+{c}+{d}+{e}=\mathrm{5} \\ $$$${Find}\:{the}\:{maximum}\:{and}\:{minimum} \\ $$$${value}\:{of}\:{S}\:=\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{d}\right)\left({d}+{e}\right)\left({e}+{a}\right) \\ $$

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