If $A$,$G$,and $H$ are the arithmetic,geometric,and harmonic means between two positive real numbers,respectively,then:

Three positive numbers form an increasing $G.P.$ If the middle term in this $G.P.$ is doubled,the new numbers are in $A.P.$ Then the common ratio of the $G.P.$ is:

If three distinct numbers $a, b, c$ are in $G.P.$ and the equations $ax^2 + 2bx + c = 0$ and $dx^2 + 2ex + f = 0$ have a common root,then which one of the following statements is correct?

Let $G$ be the geometric mean of two positive numbers $a$ and $b,$ and $M$ be the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{b}.$ If $\frac{1}{M} : G$ is $4:5,$ then $a:b$ can be

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

If $a, b, c$ are in $G.P.$ and $a + x, b + x, c + x$ are in $H.P.$,then the value of $x$ is ($a, b, c$ are distinct numbers).