Two A.M's $A_{1}$ and $A_{2}$ , two G.M's $G_{1}, G_{2}$ and two H.M's $H_{1}, H_{2}$ are inserted between any two non-zero positive numbers then $\frac{1}{H_{1}} + \frac{1}{H_{2}} =$

Open in App

Solution

Let the 2 numbers be $a, b$ then the values are;
$A_{1} = \frac{2 a + b}{3}, A_{2} = \frac{a + 2 b}{3}; G_{1} = a (\frac{b}{a})^{\frac{1}{3}}, G_{2} = a (\frac{b}{a})^{\frac{2}{3}}; H_{1} = \frac{3 a b}{a + 2 b}, H_{2} = \frac{3 a b}{2 a + b}$
$\frac{1}{H_{1}} + \frac{1}{H_{2}} = \frac{3 (a + b)}{3 a b} = \frac{a + b}{a b} = \frac{\frac{2 a + b}{3} + \frac{a + 2 b}{3}}{a (\frac{b}{a})^{\frac{1}{3}} a (\frac{b}{a})^{\frac{2}{3}}} = \frac{A_{1} + A_{2}}{G_{1} + G_{2}}$

Suggest Corrections

Similar questions

A_{1}

A_{2}

[{H_{1}}^{- 1} + {H_{2}}^{- 1}]

A_{1} a n d A_{2}

G_{1} a n d G_{2}

H_{1} a n d H_{2}

H_{1} a n d H_{2}

A_{1}, A_{2}, G_{1}, G_{2} .

Two AMs $A_{1}$ and $A_{2}$ , two GMs $G_{1}$ and $G_{2}$ and two HMs $H_{1}$ and $H_{2}$ are inserted between two numbers a and b, then

$\frac{1}{H_{1}}$ + $\frac{1}{H_{2}}$ equals.

A_{1} A_{2}; G_{1} G_{2}; H_{1} H_{2}

\frac{G_{1} G_{2}}{H_{1} H_{2}} = \frac{A_{1} + A_{2}}{H_{1} + H_{2}}

A_{1}, A_{2}, G_{1}, G_{2}

H_{1}, H_{2}

\frac{A_{1} + A_{2}}{H_{1} + H_{2}} . \frac{H_{1} H_{2}}{G_{1} G_{2}}

Join BYJU'S Learning Program