The sum of the square of the first plus twice the square of


Find two non-negative numbers whose sum is 20 and such that:

(a) The sum of their squares is:

(i) a minimum;

(ii) a maximum.

(b) The sum of the square of the first plus twice the square of the second is:

(i) minimized;

(ii) maximized.

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Mathematics: The sum of the square of the first plus twice the square of
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