The mean proportional between $$\left(9 + 4\sqrt{5}\right) \text{ and } \left(18 - 8\sqrt{5}\right) \text{ is:}$$​

Correct option is D

Given:

 $$\left(9 + 4\sqrt{5}\right) \text{ and } \left(18 - 8\sqrt{5}\right)$$

Solution: 

Mean proportional of A and B = $$\sqrt{AB}$$   

​Solution: 

​$$\left(9 + 4\sqrt{5}\right) \text{ and } \left(18 - 8\sqrt{5}\right)$$  

= $$\sqrt{\left(9 + 4\sqrt{5}\right) \left(18 - 8\sqrt{5}\right) }$$ 

= $$\sqrt{\left(9 + 4\sqrt{5}\right) \times 2\left(9- 4\sqrt{5}\right) }$$ 

= $$\sqrt{2\left(9^2 - (4\sqrt{5}\right)^2) }$$ 

= $$\sqrt{2\times (81- 80)}$$ 

= $$\sqrt{2}$$​​

​​​

​