Question

(x − 4) is geometric mean of (x − 5) and (x − 2) find x.

Answer 1

$$\begin{gathered} \left(x-4\right)\mathrm{is}\mathrm{the}\mathrm{geometric}\mathrm{mean}\mathrm{of}\left(x-5\right)\mathrm{and}\left(x-2\right). \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ {\left(x-4\right)}^2=\left(x-5\right)\times \left(x-2\right) \\ \Rightarrow x^2+16-8x=x^2-5x-2x+10 \\ \Rightarrow -8x+7x=10-16 \\ \Rightarrow -x=-6 \\ \Rightarrow x=6 \end{gathered}$$