Question

Find the geometric mean of $\sqrt{82}-1$ and $\sqrt{82}+1.$

• A. 9
• B. 3
• C. 81
• D. 27

Answer 1

The correct option is A 9

Let G be the geometric mean of $\sqrt{8}2-1$ and $\sqrt{8}2+1.$
$\therefore GM=\sqrt{\left(\right(\sqrt{82}-1\left)\right(\sqrt{82}+1\left)\right)}$
$\Rightarrow GM=\sqrt{(82-1)}\Rightarrow G=\sqrt{\left(81\right)}=9$
Hence $GM=9.$