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Minimum value of fraction with three variables

Source: Argentina Cono Sur TST 2024 P4

August 9, 2024
algebra

Problem Statement

Find the least possible value of (x2+1)(4y2+1)(9z2+1)6xyz\dfrac{(x^2+1)(4y^2+1)(9z^2+1)}{6xyz} if xx, yy, zz are not necessarily distinct positive real numbers.
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