If the aritmetic, geometric and harmonic menas between two positive real numbe

Question

If the aritmetic, geometric and harmonic menas between two positive real numbers be A, G and H, then

Options:

A .

A^{2}

= GH

B .

H^{2}

= AG

C . G = AH

D .

G^{2}

= AH

Answer: Option D
:
D

Let A = $\frac{a + b}{2}$ , G = $\sqrt{a b}$ and H = $\frac{2 a b}{a + b}$ .

Then $G^{2}$ = ab ..................(i)

and AH = $(\frac{a + b}{2}) . \frac{2 a b}{a + b}$ = ab ................(ii)

From (i) and (ii), we have $G^{2}$ = AH

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