Question

The harmonic mean of two numbers is $4$ and the arithmetic and geometric mean satisfy the relation $2A+G^2=27$, the numbers are.

• A. $6,3$
• B. $5,4$
• C. $5,-2.5$
• D. $-3,1$

Answer 1

Answer: (A)

$6,3$

Let numbers be x and y.
Then, $A=\frac{1}{2}(x+y),\sqrt{xy}=G$ or $G^2=xy$
and $\frac{2xy}{x+y}=4$
$\Rightarrow G^2=4A$
Also, $2A+G^2=2A+4A=27\Rightarrow A=\frac{9}{2}$
So, $x+y=9,xy=18$
Hence, numbers are $6$ and $3$.