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(I) Maximize Subject to the Constraint X12

Question 41

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(i) Maximize (i) Maximize subject to the constraint x<sub>1</sub><sup>2</sup> +x<sub>2</sub><sup>2</sup> + ..... x<sub>n</sub><sup>2</sup> = 1. (ii) Use part (i) to prove the well-known Arithmetic-Geometric Inequality : For any positive real numbers y1 , y2 , ....... yn , subject to the constraint x12 +x22 + ..... xn2 = 1.
(ii) Use part (i) to prove the well-known Arithmetic-Geometric Inequality :

For any positive real numbers y1 , y2 , ....... yn ,
(i) Maximize subject to the constraint x<sub>1</sub><sup>2</sup> +x<sub>2</sub><sup>2</sup> + ..... x<sub>n</sub><sup>2</sup> = 1. (ii) Use part (i) to prove the well-known Arithmetic-Geometric Inequality : For any positive real numbers y1 , y2 , ....... yn ,

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