Determine the range of values for the algebraic expression xyz. British Mathematical Olympiad

The video illustrates step-by-step how to determine the range of values for the algebraic expression xyz. To determine the range of values for xyz, we must show a ≤ xyz ≤ b. a is the lower bound, b is the upper bound. If the lower bound or the upper bound is exact, we have to show explicitly that xyz can actually take this boundary value by specifying explicit values of x, y, z that satisfy the equalities. The inequality of arithmetic and geometric means (AM-GM) is used to determine the range of values for xyz.

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