Given that \[\frac{{{a}^{3}}+3a{{b}^{2}}}{{{b}^{3}}+3{{a}^{2}}b}=\frac{63}{62}\]. Using componendo and dividendo find a : b.

It is given that

By cross multiplication

\[a\text{ }+\text{ }b\text{ }=\text{ }5a\text{ }\text{ }5b\]

We can write it as

\[\begin{array}{*{35}{l}}

5a\text{ }\text{ }a\text{ }\text{ }5b\text{ }\text{ }b\text{ }=\text{ }0  \\

4a\text{ }\text{ }6b\text{ }=\text{ }0  \\

4a\text{ }=\text{ }6b  \\

\end{array}\]

We get.

\[\begin{array}{*{35}{l}}

   a/b\text{ }=\text{ }6/4  \\

   a/b\text{ }=\text{ }3/2  \\

   \therefore a:\text{ }b\text{ }=\text{ }3:\text{ }2  \\

\end{array}\]