If a is the arithmetic mean of b and c, ...

If a is the arithmetic mean of b and c, and two geometric means `G_(1)` and `G_(2)` are inserted between b and c such that `G_(1)^(3)+G_(2)^(3)=lamda abc,` then find the value of `lamda`.

Verified by Experts

The correct Answer is:

2

Similar Questions

Explore conceptually related problems

If a is the A.M. of b and c and the two geometric means are G_1 and G_2 , then prove that G1^3+G2^3=2a b c

Insert 3 arithmetic means between 2 and 10.

If a is the A.M. of b and c and the two geometric mean are G_1 and G_2, then prove that G_1^3+G_2^3=2a b cdot

If A is the arithmetic mean and p and q be two geometric means between two numbers a and b, then prove that : p^(3)+q^(3)=2pq " A"

If a be one A.M and G_1 and G_2 be then geometric means between b and c then G_1^3+G_2^3=

If one A.M., A and two geometric means G_1a n dG_2 inserted between any two positive numbers, show that (G1 ^2)/(G2)+(G2 ^2)/(G_1)=2Adot

The arithmetic mean between two numbers is A and the geometric mean is G. Then these numbers are:

If one geometric mean G and two arithmetic means A_1a n dA_2 be inserted between two given quantities, prove that G^2=(2A_1-A_2)(2A_2-A_1)dot

If arithmetic mean of two positive numbers is A, their geometric mean is G and harmonic mean H, then H is equal to

G is the geometric mean and p and q are two arithmetic means between two numbers a and b, prove that : G^(2)=(2p-q)(2q-p)