Home
Class 11
MATHS
If a, b, c are in GP, prove that a^ 2 ...

If a, b, c are in GP, prove that a^ 2 b^ 2 c ^ 2 ( 1/ a ^ 3 +1/ b ^ 3 ​ +1/ c ^ 3 ​ )=a ^ 3 +b^ 3 +c^ 3 .

Text Solution

AI Generated Solution

To prove that \( a^2 b^2 c^2 \left( \frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{c^3} \right) = a^3 + b^3 + c^3 \) given that \( a, b, c \) are in geometric progression (GP), we can follow these steps: ### Step 1: Understand the relationship in GP Since \( a, b, c \) are in GP, we can express \( b \) in terms of \( a \) and \( c \): \[ b^2 = ac \] ...
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9K|7 Videos

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9L|10 Videos

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9I|9 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|12 Videos

  • SETS

    NAGEEN PRAKASHAN ENGLISH|Exercise MISC Exercise|16 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a^3, b^3, c^3

If (a-b),\ (b-c),(c-a) are in G.P. then prove that (a+b+c)^2=3(a b+b c+c a)

If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-1),(c^3+d^3)^(-1) are also in G.P.

If a, b, c are positive real numbers such that a + b + c = 1 , then prove that a/(b + c)+b/(c+a) + c/(a+b) >= 3/2

Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

In Figure, A D_|_B C and B D=1/3C Ddot Prove that 2C A^2=2A B^2+B C^2

Prove that : tan^(-1)( (a^3 -b^3)/(1+a^3 b^3)) + tan^(-1)( (b^3 - c^3)/(1+b^3 c^3)) + tan^(-1)( (c^3 - a^3)/(1+c^3 a^3)) = 0

If a ,b ,c are the sides of a triangle such that a : b : c=1:sqrt(3):2, then ratio A : B : C is equal to a.3:2:1 b. 3:1:2 c. 1:2:3 d. 1:3:2

If a ,b ,c are the sides of a triangle such that a : b : c=1:sqrt(3):2, then ratio A : B : C is equal to 3:2:1 b. 3:1:2 c. 1:2:3 d. 1:3:2