CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Definition of Functions

If A1 , A2...

Question

If $A_{1}, A_{2}; G_{1}, G_{2}$ and $H_{1}, H_{2}$ be two A.M.s, G.M.s and H.M.s between two quantities a and b then
prove that $A_{1} H_{2} = A_{2} H_{1} = G_{1} G_{2} = a b$

Open in App

Solution

$a, A_{1}, A_{2}, b$ are in A.P.....(1)
$a, H_{1}, H_{2}, b$ are in H.P.
$∴ \frac{1}{a}, \frac{1}{H_{1}}, \frac{1}{H_{2}}, \frac{1}{b}$ are in A.P.
Multiply by ab.
$∴ b, \frac{a b}{H_{1}}, \frac{a b}{H_{2}}, a$ are in A.P
Take in reverse order
Or $∴ a, \frac{a b}{H_{2}}, \frac{a b}{H_{a}}, b$ ......(2)
Compare (1) and (2)
$A_{1} = \frac{a b}{H_{2}} a n d A_{2} = \frac{a b}{H_{1}}$
$∴ A_{1} H_{2} = A_{2} H_{1} = a b = G_{1} G_{2}$

Suggest Corrections

thumbs-up

0

Similar questions

A_{1}, A_{2}; G_{1}, G_{2} a n d H_{1}, H_{2}

be two A.M.s, G.M.s and H.M.s between two quantities '

a

b

A_{1} H_{2} = A_{2} H_{1} = G_{1} G_{2}

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

H_{1}, H_{2}

be two A.M.s, G.M.s and H.M.s between two quantities a and b then
prove that

\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}

be two A.M.s, G.M.s and H.M.s between two numbers then prove:

\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}

are two A.Ms, G.Ms and H.M.s between two numbers, then

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

G_{1}, G_{2}

H_{1,} H_{2}

be two A.Ms and H.M.s between two quantities, then the value of

\frac{G_{1} G_{2}}{H_{1} H_{2}}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Definition of Function

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Definition of Functions

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon