Question

How do i solve this with explanation please

Answer 1

`a = 100`

Explanation:

The geometric mean (
`x`) of two numbers (
`a` and
`b`) is defined as:

`x = √(a \cdot b\,)`

Using this model, we can write the geometric mean of
`a` and
`68` as:

`x = √(a \cdot 68\,)`

In this equation, we can replace
`x` with the given geometric mean,
`20√(17\,)`:

`20√(17\,) = √(a \cdot 68\,)`

From here, we can solve for
`a` using algebraic manipulation.

↓ squaring both sides

`\left(\frac{}{}20√(17\,)\frac{}{}\right)^2 = \left(\frac{}{}√(a \cdot 68\,)\frac{}{}\right)^2`

`20^2 \cdot 17 = a \cdot 68`

`6800 = a \cdot 68`

↓ dividing both sides by
`68`

`\underline{6800} = \underline{a \cdot 68} \\ \text{ } \: 68 \ \ \ \ \ \ \ 68`

`\boxed{a = 100}`