Find Two Positive Numbers Whose Sum Is $62$ And the Sum of Whose Squares Is a Minimum

question 142

Essay

Find two positive numbers whose sum is $62$ and the sum of whose squares is a minimum.

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Definitions:

Mound-Shaped

Mound-shaped describes a symmetrical, bell-shaped distribution of data points, indicative of a normal distribution.

Mode

The value that appears most frequently in a data set, a measure of central tendency.

Proportion of Weights

The ratio of an individual weight to the total weight of all items combined, often used in statistical calculations to determine relative importance.

Tchebysheff's Theorem

A statistical rule stating that for any set of data, no matter the distribution, a certain proportion of values will fall within a specified number of standard deviations from the mean.