It is given that
a, b, c are in continued proportion
So we get
a/b = b/c = k
(iii) \[~a:\text{ }c\text{ }=\text{ }({{a}^{2}}~+\text{ }{{b}^{2}}):\text{ }({{b}^{2}}~+\text{ }{{c}^{2}})\]
We can write it as
Therefore, LHS = RHS.
(iv) \[{{a}^{2}}{{b}^{2}}{{c}^{2}}~({{a}^{-4}}~+\text{ }{{b}^{-4}}~+\text{ }{{c}^{-4}})\text{ }=\text{ }{{b}^{-2}}~({{a}^{4}}~+\text{ }{{b}^{4}}~+\text{ }{{c}^{4}})\]
Therefore, LHS = RHS.