Question

Given that ${\displaystyle \frac{a^3+3a{b}^2}{b^2+3a^{2}b}=\frac{63}{62}}$.
Using Componendo and Dividendo find a : b.

Answer 1

We have
${\displaystyle \frac{a^3+3a{b}^2}{b^2+3a^{2}b}=\frac{63}{62}}$
App. compoenedo  and dividendo
${\displaystyle \frac{a^3+3a{b}^2+b^3+3a^{2}b}{a^3+3a{b}^2-b^3-3a^{2}b}=\frac{63+62}{63-62}}$
${\displaystyle \frac{a^3+3a{b}^2+b^3+3a^{2}b}{a^3+3a{b}^2-b^3-3a^{2}b}=\frac{125}{1}}$
${\displaystyle \frac{{(a+b)}^3}{{(a-b)}^3}=\frac{125}{1}}$
${\displaystyle \frac{a+b}{a-b}=\frac{5}{1}}$
Again Applying Componendo & Dividendo
${\displaystyle \frac{a+b+a-b}{a+b-a+b}=\frac{5+1}{5-1}}$
${\displaystyle \frac{2a}{2b}=\frac{6}{4}}$
a : b = 3 : 2