Let `alpha` and `beta` be two positive real numbers. Suppose `A_1, A_2` are two arithmetic means; `G_1 ,G_2` are tow geometrie means and `H_1 H_2` are two harmonic means between `alpha` and `beta`, then

Let alpha and beta be two positive real numbers. Suppose A_1, A_2 are two arithmetic means; G_1 ,G_2 are two geometric means and H_1 H_2 are two harmonic means between alpha and beta , then

Let a ,b be positive real numbers. If a A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)=((2a+b)(a+2b))/(9a b)

Let a ,b be positive real numbers. If a A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)=((2a+b)(a+2b))/(9a b)

Let a ,b be positive real numbers. If a A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)=((2a+b)(a+2b))/(9a b)

Let a ,b be positive real numbers. If a, A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)

Let a ,b be positive real numbers. If a, A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)

If two positive values of a variable be x_(1) and x_(2) and the arithmetic mean be A, geometric mean be G and the harmonic mean be H, then prove that G^(2)=AH

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

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

If A, G and H are the arithmetic mean, geometric mean and harmonic mean between unequal positive integers. Then, the equation Ax^2 -|G|x- H=0 has