Question 3
Real numbers $x_1,x_2,x_3,x_4$ satisfy $\tfrac12\le x_1^2+x_2^2+x_3^2+x_4^2\le1$. Find the greatest and least values of
$$A=(x_1-2x_2+x_3)^2+(x_2-2x_3+x_4)^2+(x_2-2x_1)^2+(x_3-2x_4)^2.$$
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; the rubric is editorial. Importer multipliers: correct 1, incorrect 0, blank 0.
$$A=(x_1-2x_2+x_3)^2+(x_2-2x_3+x_4)^2+(x_2-2x_1)^2+(x_3-2x_4)^2.$$
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; the rubric is editorial. Importer multipliers: correct 1, incorrect 0, blank 0.