Question

If √6 is the geometric mean between 6 and another number, then the number is
1
2
6

Answer 1

\[\frac{a}{\sqrt{6}}=\frac{\sqrt{6}}{b}\\so\\ab=6\\\]
one of a,b =6 so other is ...?

Answer 2

ab = 6
as in
a x b = 6? @amoodarya

Answer 3

yes
a*b=6
and
for example a=6
so ...

Answer 4

ah so find an a and b such that it equals to 6

so for your example a = 6

6b=6

solving for b gives me 1
so
(6)(1) = 6
6=6

Answer 5

\[1,\sqrt{6},6\\or \\6,\sqrt{6},1\]

Answer 6

so there's more than one answer to this.
\[(\sqrt{6})(\sqrt{6} )=6\]
6=6

Answer 7

the geometric mean of \(a,b\) is \(\sqrt{ab}\) so here we have \(\sqrt6=\sqrt{6x}\implies x=1\)

Answer 8

a,b>=0 or a,b<=o