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Solve the problem by the method of lagrange

Question: Solve the problem

max_x,y,z 2x - 2y + z s.t. x² + y² + z² = 9

by the method of Lagrange multipliers. Use the sufficient second-order conditions for a strict maximum to determine which of the two solutions to the system of first-order conditions yields a maximum. Verify that this is correct by comparing the values of the objective function in both cases.

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Mathematics: Solve the problem by the method of lagrange

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