Insert a geometric mean between k and 1/k.

To insert a geometric mean between \( k \) and \( \frac{1}{k} \), we use the formula for the geometric mean of two numbers \( a \) and \( b \), which is:

\[
\text{Geometric Mean} = \sqrt{a \times b}
\]

Here, \( a = k \) and \( b = \frac{1}{k} \). So, the geometric mean is:

\[
\text{Geometric Mean} = \sqrt{k \times \frac{1}{k}} = \sqrt{1} = 1
\]

Thus, the geometric mean between \( k \) and \( \frac{1}{k} \) is 1.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find multiple geometric means between two numbers?
2. What is the difference between arithmetic mean and geometric mean?
3. How is the geometric mean used in finance or growth calculations?
4. Can the geometric mean be negative?
5. How does the geometric mean change if both numbers are negative?

**Tip**: The geometric mean is useful in comparing ratios or percentages, especially in cases involving growth rates or proportions.

Learn how to insert a geometric mean between k and 1/k using the geometric mean formula √(a × b). This problem involves key algebraic concepts and is suitable for students in Grades 9-11.

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