Question

geometric mean of x and x7​

Answer 1

Answer:

x^4

hope it helpful......

Answer 2

SOLUTION

TO DETERMINE

$\sf The \: geometric \: mean \: of \: \: x \: \: and \: \: {x}^{7}$

CONCEPT TO BE IMPLEMENTED

If a and b are two given numbers then the Geometric mean between a and b is

$\sf{ = \sqrt{ab} }$

EVALUATION

$\sf Let \: y \: be \: the \: geometric \: mean \: of \: \: x \: \: and \: \: {x}^{7}$

So by the given condition

$\displaystyle \sf{ \frac{x}{y} = \frac{y}{ {x}^{7} } }$

$\displaystyle \sf{ \implies \: {y}^{2} = {x}^{8} }$

$\displaystyle \sf{ \implies \: {y}^{} = {x}^{4} }$

FINAL ANSWER

$\sf The \: geometric \: mean \: of \: \: x \: \: and \: \: {x}^{7} \: is \: \: {x}^{4}$

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