If A, G and H are respectively the A.M., the G.M. and the H.M. between two positive numbers a and b, then the correct relation is

Question

If A, G and H are respectively the A.M., the G.M. and the H.M. between two positive numbers $a$ and $b$ , then the correct relation is

Smart Achievers · Accepted Answer

(4)

$For positive numbers a and b,$

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

$Now,$ $A H = \frac{a + b}{2} (\frac{2 a b}{a + b}) = a b = G^{2}$

$∴$ $The correct relation is, G^{2} = A H$

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