The mean proportional between 9 + $$3\sqrt{7}$$ and 18 – $$6\sqrt{7}$$ is:​

Correct option is A

Given:

We are to find the mean proportional between:

​$$9 + 3\sqrt{7} \quad \text{and} \quad 18 - 6\sqrt{7}$$​​

Formula Used:

The mean proportional between two numbers a and b is:

= $$\sqrt{a \cdot b}$$​​

Solution:  

Mean Proportional = $$\sqrt{(9 + 3\sqrt{7})(18 - 6\sqrt{7})}$$ 

$$=\sqrt{2(9 + 3\sqrt{7})(9 - 3\sqrt{7})} \\ \ \\ = \sqrt{2\{(9)^2 - (3\sqrt{7})^2\}}\\ \ \\ = \sqrt{2\{81 - 63\}}\\ \ \\ = \sqrt{2\{18\}} \\ \ \\ = \sqrt{2\times 3\times 3\times 2} \\ \ \\ = 6$$​​