Home
Class 11
MATHS
If the arithmetic mean between two posit...

If the arithmetic mean between two positive numbers is n(>1) times the geometric mean between them, show that the ratio of the greater number to the smaller is `(n+sqrt(n^2-1))/(n-sqrt(n^2-1))`.

Promotional Banner

Similar Questions

Explore conceptually related problems

If the harmonic mean between two positive numbers is to their geometric mean as 12: 13. then the numbers are in the ratio

If the arithmetic means of two positive number a and b (a gt b ) is twice their geometric mean, then find the ratio a: b

Prove that the sum of n arithmetic means between two numbers is n times the single A.M. between them.

The A.M. between two distinct positive numbers is twice the G.M. between them. Find the ratio of the greater to the smaller.

If the geometric mea is (1)/(n) times the harmonic mean between two numbers, then show that the ratio of the two numbers is 1+sqrt(1-n^(2)):1-sqrt(1-n^(2)) .

The arithmetic mean of first n odd natural numbers is :

Suppose p is the first of n(ngt1) arithmetic means between two positive numbers a and b and q the first of n harmonic means between the same two numbers. The value of p is

Suppose p is the first of n(ngt1) arithmetic means between two positive numbers a and b and q the first of n harmonic means between the same two numbers. The value of q is

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio (3+2sqrt2):(3-2sqrt2) .

If G is the geometric mean between two distinct positive numbers a and b, then show that 1/(G-a)+1/(G-b)=1/G .