Question

Insert $2$ geometric means between $3$ and $81$.

Answer 1

$3$ & $81$

$\Rightarrow 3,x,y,81$

$3y=x^2$ $x\times 81=y^2$

$9y^2=x^2$ $y^2=81x$

$9\times 81x=x^4$ $y^2=3^4\cdot 3^2$

$(x=9)$ $(y=2y)$ $(\therefore 3,9,27,81)$.