In this problem, let us try to maximize the function J = |3x+2y-7z| under the constraint of 2x+y+3z = 5, by applying the Cauchy-Schwarz inequality.

In this problem, let us try to maximize the function J = |3x+2y-7z| under the constraint of 2x²+y²+3z² = 5, by applying the Cauchy-Schwarz inequality. The trick is to view J as the absolute value of the inner product of u?=(?2x, y, ?3z) and y = (3/?2,2, -7/?3). Find the maximum value of J.