The number of triples $(x, y, z)$ of real numbers satisfying the equation $x^4+y^4+z^4+1=4 x y z$ is

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

Let $A, G$ and $H$ be the arithmetic mean, geometric mean and harmonic mean, respectively of two distinct positive real numbers. If $\alpha$ is the smallest of the two roots of the equation $A(G-H) x^2+G(H-A) x$ $+H(A-G)=0$ then,

Let $A_1$ and $A_2$ be two arithmetic means and $G_1, G_2$, $G _3$ be three geometric means of two distinct positive numbers. The $G _1^4+ G _2^4+ G _3^4+ G _1^2 G _3^2$ is equal to

If $a,\;b,\;c$ are in $A.P.$, then $\frac{a}{{bc}},\;\frac{1}{c},\;\frac{2}{b}$ are in

In the four numbers first three are in $G.P.$ and last three are in $A.P.$ whose common difference is $6$. If the first and last numbers are same, then first will be