Mathematics: If the geometric mean of a and 34 is 6 sqrt(17) find the value of a

If the geometric mean of a and 34 is 6 sqrt(17) - id3461714083143, valenzueladomipay09u

Destinyb9806

16.09.2021

Using the geometric mean concept, it is found that the value of a is 18.

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The geometric mean, of a data-set of n elements, (n_1, n_2, ..., n_n) , is given by:

$G = \sqrt[n]{n_1 \times n_2 \times ... \times n_n}$

That is, the nth root of the multiplication of all elements.

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In this question:

Two elements(n = 2), a and 34. $G = 6\sqrt{17}$

Thus:

$\sqrt{34a} = 6\sqrt{17}$

We find the square of each side, so:

$(\sqrt{34a})^2 = (6\sqrt{17})^2$

$34a = 36\times17$

Simplifying both sides by 17:

2a = 36

$a = \frac{36}{2}$

a = 18

The value of a is 18.

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