If $a, b, c$ are in both Arithmetic Progression $(A.P.)$ and Geometric Progression $(G.P.)$,then......

Let $0 < z < y < x$ be three real numbers such that $\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ are in an arithmetic progression and $x, \sqrt{2}y, z$ are in a geometric progression. If $xy + yz + zx = \frac{3}{\sqrt{2}} xyz$,then $3(x + y + z)^2$ is equal to $............$.

If the arithmetic and geometric means of $a$ and $b$ are $A$ and $G$ respectively,then the value of $A - G$ is

If the $A.M.$ is twice the $G.M.$ of the numbers $a$ and $b$,then $a:b$ will be

If the ratio of the harmonic mean to the geometric mean of two positive numbers $a$ and $b$ $(a > b)$ is $4 : 5$,then $a : b = \dots$ (in $: 1$)

If the ratio of $H.M.$ and $G.M.$ between two numbers $a$ and $b$ is $4:5$,then the ratio of the two numbers will be