Question

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

Answer 1

$\frac{a^3+3a{b}^2}{b^3+3a^{2}b}=\frac{63}{62}$

$\Rightarrow \frac{a^3+3a{b}^2+3a^{2}b+b^3}{a^3+3a{b}^2-3a^{2}b-b^3}=\frac{63+62}{63-62}$

$\Rightarrow \frac{(a+b{)}^3}{(a-b{)}^3}=125$

$\Rightarrow \frac{a+b}{a-b}=5$ $\Rightarrow a+b=5a-5b$

$\Rightarrow 6b=4a$

$\Rightarrow \frac{a}{b}=\frac{6}{4}=\frac{3}{2}$