## anonymous one year ago If √6 is the geometric mean between 6 and another number, then the number is 1 2 6

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1. amoodarya

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

2. UsukiDoll

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

3. amoodarya

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

4. 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

5. amoodarya

$1,\sqrt{6},6\\or \\6,\sqrt{6},1$

6. UsukiDoll

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

7. anonymous

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

8. anonymous

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