Question

If the arithmetic mean of two numbers is $5$ and geometric mean is $4$, then the numbers are

• A. $4,6$
• B. $4,7$
• C. $3,8$
• D. $2,8$

Answer 1

The correct option is D $2,8$

Let $x,y$ be the numbers
$\therefore \frac{x+y}{2}=5$ and $\sqrt{xy}=4$
$\Rightarrow xy=16$
$\therefore x+y=10,xy=16$
$\Rightarrow (x-y{)}^2=(x+y{)}^2-4xy=100-64=36$
$\Rightarrow x-y=6$
$\therefore x=8,y=2$