if-aa-bb-ab-ba-1-7-then-faind-a-b-

Question Number 131429 by mathlove last updated on 04/Feb/21

i f \frac{a a - b b}{a b + b a} = \frac{1}{7} t h e n f a i n d \frac{a}{b} = ?

Answered by Dwaipayan Shikari last updated on 04/Feb/21

\frac{a^{2} - b^{2}}{2 a b} = \frac{1}{7} \Rightarrow (\frac{a}{b}) - (\frac{b}{a}) = \frac{2}{7} \Rightarrow \frac{a}{b} = \frac{- \frac{2}{7} \pm \sqrt{\frac{4}{49} + 4}}{2}

= \frac{- 1 \pm 5 \sqrt{2}}{7}