For-a-b-c-0-if-a-b-c-n-determine-minimum-and-maximum-values-of-a-2-b-2-c-2-ab-bc-ca-

Question Number 32767 by Rasheed.Sindhi last updated on 01/Apr/18

For a, b, c ⩾ 0 if a + b + c = n, determine

minimum and maximum values of

a^{2} + b^{2} + c^{2} - a b - b c - c a .

Commented by Rasheed.Sindhi last updated on 02/Apr/18

Is it correct

a + b + c ⩽ a^{2} + b^{2} + c^{2} - a b - b c - c a ⩽ {(a + b + c)}^{2}

?

Commented by mrW2 last updated on 05/Apr/18

0 ⩽ a^{2} + b^{2} + c^{2} - a b - b c - c a ⩽ n^{2}

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