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

6,3

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5,4

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5, -2.5

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-3,1

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Solution

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

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The harmonic mean of two numbers is 4 and the arithmetic and geometric means satisfy the relation 2A+G2=27, the numbers are

The correct option is A 6,3Let numbers be x and y. Then A=12(x+y),√xy=G or G2=xy and 2xy(x+y)=4, ⇒G2=4A Also, 2A+G2=2A+4A=27⇒A=92 So, x+y=9,xy=18 Hence numbers are 6,3.

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

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