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Q.

$x, y$ are two real numbers. If A is half of their sum, G is root of their product and H is average of their reciprocals then

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a

$A = G + H$

b

$G = A . H$

c

$A . H = G^{2}$

d

$A = H G^{2}$

answer is C.

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Detailed Solution

$x, y$ are two real number

$A = \frac{x + y}{2}$

$G = \sqrt{x y}$

$H = \frac{1}{2} [\frac{1}{x} + \frac{1}{y}] = \frac{x + y}{2 x y}$

$\frac{A}{H} = \frac{x + y}{2} \times \frac{2 x y}{x + y} = x y = G^{2}$

$A = H G^{2}$

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x,y are two real numbers. If A is half of their sum, G is root of their product and H is average of their reciprocals then