Consider two positive numbers $a$ and $b$ . If arithmetic mean of $a$ and $b$ exceeds their geometric mean by $\frac{3}{2}$ and geometric mean of $a$ and $b$ exceeds their harmonic mean by $\frac{6}{5}$ , then the absolute value of $(a^2 -b^2)$ is equal to

If the arithmetic, geometric and harmonic means between two distinct positive real numbers be $A,\;G$ and $H$ respectively, then the relation between them is

The number of different possible values for the sum $x+y+z$, where $x, y, z$ are real number such that $x^4+4 y^4+16 z^4+64=32 x y z$ is

The reciprocal of the mean of the reciprocals of $n$ observations is their

If $a,\;b,\;c$ are in $G.P.$ and $x,\,y$ are the arithmetic means between $a,\;b$ and $b,\;c$ respectively, then $\frac{a}{x} + \frac{c}{y}$ is equal to

The harmonic mean between two numbers is $14\frac{2}{5}$ and the geometric mean $24$ . The greater number them is