*For what positive number \(x\) is the \(x\)-th root of \( x\) the greatest?*

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*The author states a "Master Theorem" from which, exploiting concavity, he deduces several classical inequalities.*

*The creation of 'extriangles' based on a given triangle is iterated, giving rise to four quadrilaterals each with area five times the area of the original triangle.*