Let a and b be two distinct positive num...

Let a and b be two distinct positive numbers such that `a gt b`. If the G.M between them is `m( gt 1)` times the H.M between them , then prove that `a : b =m+sqrt(m^(2)-1) : m-2sqrt(m^(2)-1)`

Similar Questions

Explore conceptually related problems

If the A.M between a and b is m times their H.M then a:b is

If the ratio of A.M. and G.M. of two positive numbers a and b is m : n, then prove that : a:b=(m+sqrt(m^(2)-n^(2))):(m-sqrt(m^(2)-n^(2)))

If A.M.and G.M.between two numbers is in the ratio m:n then prove that the numbers are in the ratio (m+sqrt(m^(2)-n^(2))):(m-sqrt(m^(2)-n^(2)))

Suppose A.M. of two positive numbers be 7 and G.M. between them be 5. The A.M. between their squares is

If a is the A.M. between b and c, b the G.M. between a and c, then show that 1/a,1/c,1/b are in A.P.

If sum of two numbers a&b is n xx their G.M then show that (a)/(b)=(n+sqrt(n^(2)-4))/(n-sqrt(n^(2)-4))

The ratio of the A.M.and G.M.of two positive numbers a and b,is : n .Show that a :b=(m+sqrt(m^(2)-n^(2))):(m-sqrt(m^(2)-n^(2)))

If A and G be the A .M and G.M between two positive numbers, then the numbers are