Question

find the mean proportional to 7/125 and 5/343​

Answer 1

SOLUTION

TO DETERMINE

The mean proportional to

$\displaystyle \sf{ \frac{7}{125} \: \: and \: \: \frac{5}{343} }$

EVALUATION

Let x be the mean proportional to

$\displaystyle \sf{ \frac{7}{125} \: \: and \: \: \frac{5}{343} }$

Then by the given condition

$\displaystyle \sf{ \frac{7}{125} : x = x: \: \: \frac{5}{343} }$

$\displaystyle \sf{ \implies \: \frac{ \frac{7}{125} }{x}= \frac{x}{ \frac{5}{343}} \: \: }$

$\displaystyle \sf{ \implies \: {x}^{2} = \frac{7}{125} \times \frac{5}{343} \: }$

$\displaystyle \sf{ \implies \: {x}^{2} = \frac{1}{25} \times \frac{1}{49} \: }$

$\displaystyle \sf{ \implies \: x = \pm \: \frac{1}{5} \times \frac{1}{7} \: }$

$\displaystyle \sf{ \implies \: x = \pm \: \frac{1}{35} \: }$

FINAL ANSWER

Hence the required mean proportional is

$\displaystyle \sf{ - \frac{1}{35} \: \: \: or \: \: \: \frac{1}{35} }$

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