If $a, b, c$ are in $A.P.$ and $b, c, d$ are in $H.P.$,then

If ${b^2}, {a^2}, {c^2}$ are in $A.P.$,then $a + b, b + c, c + a$ will be in

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?

The sum of two numbers is $6$ times their geometric mean. Show that the numbers are in the ratio $(3+2 \sqrt{2}):(3-2 \sqrt{2})$.

If the arithmetic mean between $p$ and $q$ $(p > q)$ is twice the geometric mean,then $p : q = .......$

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