anonymous
  • anonymous
If √6 is the geometric mean between 6 and another number, then the number is 1 2 6
Geometry
katieb
  • katieb
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amoodarya
  • amoodarya
\[\frac{a}{\sqrt{6}}=\frac{\sqrt{6}}{b}\\so\\ab=6\\\] one of a,b =6 so other is ...?
UsukiDoll
  • UsukiDoll
ab = 6 as in a x b = 6? @amoodarya
amoodarya
  • amoodarya
yes a*b=6 and for example a=6 so ...

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UsukiDoll
  • UsukiDoll
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
amoodarya
  • amoodarya
\[1,\sqrt{6},6\\or \\6,\sqrt{6},1\]
UsukiDoll
  • UsukiDoll
so there's more than one answer to this. \[(\sqrt{6})(\sqrt{6} )=6\] 6=6
anonymous
  • anonymous
the geometric mean of \(a,b\) is \(\sqrt{ab}\) so here we have \(\sqrt6=\sqrt{6x}\implies x=1\)
anonymous
  • anonymous
a,b>=0 or a,b<=o

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