Question

If (a + b + c) (a $-$ b + c) = a² + b² + c² show that a, b, c are in continued proportion.

Answer 1

$$\begin{gathered} \left(a+b+c\right)\left(a-b+c\right)=a^2+b^2+c^2 \\ \Rightarrow {\left(a+c\right)}^2-b^2=a^2+b^2+c^2 \\ \Rightarrow a^2+c^2+2ac-b^2=a^2+b^2+c^2 \\ \Rightarrow 2b^2=2ac \\ \Rightarrow b^2=ac \end{gathered}$$
Therefore, a, b, c are in continued proportion.