The geometric and harmonic means of two numbe | vedclass

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(C) Let the two numbers be $x_1$ and $x_2$.The geometric mean $GM = \sqrt{x_1 x_2} = 18$,so $x_1 x_2 = 18^2 = 324$.The harmonic mean $HM = \frac{2x_1

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$15$

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(C) Let the two numbers be $x_1$ and $x_2$.The geometric mean $GM = \sqrt{x_1 x_2} = 18$,so $x_1 x_2 = 18^2 = 324$.The harmonic mean $HM = \frac{2x_1 x_2}{x_1 + x_2} = 16\frac{8}{13} = \frac{216}{13}$.Substituting $x_1 x_2 = 324$ into the $HM$ formula: $\frac{2(324)}{x_1 + x_2} = \frac{216}{13}$.$x_1 + x_2 = \frac{648 	imes 13}{216} = 3 	imes 13 = 39$.Now,we know $(x_1 - x_2)^2 = (x_1 + x_2)^2 - 4x_1 x_2$.$(x_1 - x_2)^2 = (39)^2 - 4(324) = 1521 - 1296 = 225$.Therefore,$|x_1 - x_2| = \sqrt{225} = 15$.

The geometric and harmonic means of two numbers $x_1$ and $x_2$ are $18$ and $16\frac{8}{13}$ respectively. The value of $|x_1 - x_2|$ is

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