Question Number 131429 by mathlove last updated on 04/Feb/21
$${if}\:\:\:\:\frac{{aa}−{bb}}{{ab}+{ba}}=\frac{\mathrm{1}}{\mathrm{7}}\:\:\:\:\:\:\:\:\:{then}\:{faind}\:\frac{{a}}{{b}}=? \\ $$
Answered by Dwaipayan Shikari last updated on 04/Feb/21
$$\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{2}{ab}}=\frac{\mathrm{1}}{\mathrm{7}}\Rightarrow\left(\frac{{a}}{{b}}\right)−\left(\frac{{b}}{{a}}\right)=\frac{\mathrm{2}}{\mathrm{7}}\Rightarrow\frac{{a}}{{b}}=\frac{−\frac{\mathrm{2}}{\mathrm{7}}\pm\sqrt{\frac{\mathrm{4}}{\mathrm{49}}+\mathrm{4}}}{\mathrm{2}} \\ $$$$=\frac{−\mathrm{1}\pm\mathrm{5}\sqrt{\mathrm{2}}}{\mathrm{7}} \\ $$