### The average of two numbers is 6.5 and square root of their product is 6. What are the numbers?

A. 11 and 2 B. 8 and 5 C. 9 and 4 D. 10 and 3 Answer: Option C
$\begin{array}{l}\text{Let the two numbers be x and y}\\ \text{Then,}\\ x+y=6.5\times2=13\text{ and }\\ \sqrt{xy}=6\text{ or }xy=36\\ \Rightarrow(x-y)^2=(x+y)^2-4xy\\ \Rightarrow(x-y)^2=(13)^2-4\times36\\ \Rightarrow(x-y)^2=169-144\\ \Rightarrow(x-y)^2=25\\ \Rightarrow(x-y)=5\\ \text{ Solving }x+y=13\text{ and }x-y=5\\ \text{ We get }:x=9,y=4\end{array}$