CameraIcon

SearchIcon

MyQuestionIcon

1

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

Geometric Mean

If a be one...

Question

If $a$ be one A.M and $G_{1}$ and $G_{2}$ be the G.Ms between $b$ and $c$ then $G_{1}^{3} + G_{2}^{3} =$

A

a b c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

2 a b c

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

3 a b c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

4 a b c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $2 a b c$
Lets consider $b = p^{3}, c = q^{3}$
$G 1 = p^{2} q$
$G 2 = p q^{2}$
$(G 1)^{3} + (G 2)^{3} = (p q)^{3} [p^{3} + q^{3}]$
$= b c (b + c)$
$a = (b + c) / 2$
$2 a = b + c$
So the expression for $(G 1)^{3} + (G 2)^{3} = 2 a b c$
Option B

Suggest Corrections

thumbs-up

0

Similar questions

a

be the A.M of two numbers

b

c

G_{1}, G_{2}

are the two G.Ms between them then prove that

G_{1}^{3} + G_{2}^{3} = 2 a b c

b

c

a

and the two geometric means between them are

G_{1}

G_{2}

, then the value of

G_{1}^{3} + G_{2}^{3}

If p,q be two A.M.'s and G be one G.M. between two numbers, then $G^{2} =$

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}}

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}}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Geometric Progression

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon