How do i solve this with explanation please

Question

asked Oct 16, 2024 178k views

1 Answer

Murtaza Haji · Answer 1 · 2024-10-21T11:13:38+0000

Answer:

a = 100

Explanation:

The geometric mean (
) of two numbers (
and
) is defined as:

$x = √(a \cdot b\,)$

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

$x = √(a \cdot 68\,)$

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

$20√(17\,) = √(a \cdot 68\,)$

From here, we can solve for
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

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

$\boxed{a = 100}$