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, [tex](n_1, n_2, ..., n_n)[/tex], is given by:
[tex]G = \sqrt[n]{n_1 \times n_2 \times ... \times n_n}[/tex]
That is, the nth root of the multiplication of all elements.
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In this question:
Thus:
[tex]\sqrt{34a} = 6\sqrt{17}[/tex]
We find the square of each side, so:
[tex](\sqrt{34a})^2 = (6\sqrt{17})^2[/tex]
[tex]34a = 36\times17[/tex]
Simplifying both sides by 17:
[tex]2a = 36[/tex]
[tex]a = \frac{36}{2}[/tex]
[tex]a = 18[/tex]
The value of a is 18.
A similar example is given at https://brainly.com/question/15010240
