Home
Class 12
MATHS
If m is the A.M. of two distinct real...

If m is the A.M. of two distinct real numbers `l` and `n""(""l ,""n"">""1)` and G1, G2 and G3 are three geometric means between `l` and n, then `G1 4+2G2 4+G3 4` equals, (1) `4l^2` mn (2) `4l^m^2` mn (3) `4l m n^2` (4) `4l^2m^2n^2`

A

`4 l^2 mn `

B

`4 lm^2 n`

C

`4 lmn^2`

D

`4l^2m^n^2`

Text Solution

Verified by Experts

The correct Answer is:
B
`m=(l+n)/2`
and `l,G_(1),G_(2),G_(3),n` are in G.P.
`therefore r=(n/l)^(1//4)`
`thereforeG_(1)=l(n/l)^(1//4),G_(2)=l(n/l)^(1//2),G_(3)=l(n/l)^(3//4)`
`(G_(1))^(4)+2(G_(2))^(4)+(G_(3))^(4)`
`=l^(4)(n/l)+2l^(4)(n/l)^(2)+l^(4)(n/l)^(3)`
`l^(3)n+2l^(2)n^(2)+ln^(3)`
`=nl(l^(2)+2nl+n^(2))`
`=nl(l+n)^(2)`
`=4m^(2)nl`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise JEE Advanced Previous Year|16 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Numerical)|28 Videos

  • PROBABILITY II

    CENGAGE|Exercise NUMARICAL VALUE TYPE|2 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

If m is the A.M. of two distinct real numbers l and n""(""l ,""n"">""1) and G_1, G_2 and G_3 are three geometric means between l and n, then G_1^4+2G_2^4+G_3^4 equals, (1) 4l^2 mn (2) 4l^m^2 mn (3) 4l m n^2 (4) 4l^2m^2n^2

If m is the AM of two distinct real numbers l and n (l,ngt1) and G_(1),G_(2)" and "G_(3) are three geometric means between l and n, then G_(1)^(4)+2G_(2)^(4)+G_(3)^(4) equals

If m is the A.M.of two distinct real numbers l and n(l,n>1) and G_(1),G_(2) and G_(3) are three geometric means between I and n then G_(1)^(4)+2G_(2)^(4)+G_(3)^(4) equals-

if m is the AM of two distinct real number l and n and G_(1),G_(2) and G_(3) are three geometric means between l and n, then (G_(1)^(4)+G_(2)^(4)+G_(3)^(4)) equals to

(2n+1) G.M.s are inserted between 4 and 2916 .Then the (n+1)^(th) G.M.is equal to

Let l, m and n are three distinct numbers in arithmetic progression. Also l^(2) , m^(2) and n^(2) are in geometric prgression and l+m+n=3 . If l lt m lt n , then n is equal to

Factoris the expression. l ^(2) m ^(2) n - lm ^(2) n ^(2) - l^(2) mn ^(2)

If l,m,n are the direction cosines of the line x-1=2(y+3)=1-z , then what is l^4+m^(4)+n^(4) equal to?

Write the greatest common factor in each of the term. l ^(2) m ^(2) n, l m ^(2) n ^(2) , l ^(2) mn ^(2)