Question

find Geometric mean between 4 and 16

Answer 1

Answer:

The geometric mean is defined as the nth root of the p roduct of n numbers. The geometric mean of 4 and 16 is 8.

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Answer 2

SOLUTION

TO DETERMINE

The Geometric mean between 4 and 16

EVALUATION

Let x be the Geometric mean between 4 and 16

Then 4 , x , 16 are in Geometric Progression

So by the given condition

$\displaystyle \sf{ \frac{x}{4} = \frac{16}{x} }$

$\displaystyle \sf{ \implies {x}^{2} = 64 }$

$\displaystyle \sf{ \implies x = \pm \sqrt{64} }$

$\displaystyle \sf{ \implies x = \pm 8 }$

Hence the required Geometric mean between 4 and 16 are - 8 , 8

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