Question

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

Answer 1

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.

A similar example is given at brainly.com/question/15010240