Question

If the geometric mean of a and 12 is 8root6, find the value of a.

Answer 1

The value of a, when the geometric mean of two numbers a and 12 is 8√6 is equal to the number 32.

How to find geometric mean?

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

For Geometric sequence, the value of  geometric mean can be found out using the following formula,

$x=\sqrt{ab}$

Here, (a and b) are the two terms of geometric sequence.

The geometric mean of a and 12 is 8√6. Thus,

$x=8\sqrt{6}$

$b=12$

Put this value in formula to find the value of a,

$8\sqrt{6}=\sqrt{a\times12}$

Square both side of equation,

$(8\sqrt{6})^2=(\sqrt{a\times12})^2\\64\times6=12a\\a=\dfrac{64\times6}{12}\\a=32$

Thus, the value of a, when the geometric mean of two numbers a and 12 is 8√6 is equal to the number 32.

Learn more about the geometric sequence here;

https://brainly.com/question/1509142

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