Using Lagrange's Multipliers, deduce that if #1, #2,..., n are positive numbers, then VI1I2... In n...

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Using Lagrange's Multipliers, deduce that if #1, #2,..., n are positive numbers, then VI1I2... In n i=1 Xi. In other words, this inequality says that the geometric mean of n numbers is no larger than the arithmetic mean of the numbers. Using Lagrange's Multipliers, deduce that if #1, #2,..., n are positive numbers, then VI1I2... In n i=1 Xi. In other words, this inequality says that the geometric mean of n numbers is no larger than the arithmetic mean of the numbers.

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