Question

a/b=b/a-2. Find- a^2 / b^2 + b^2 / a^2​

Answer 1

given:-

$\frac{a}{b} = \frac{b}{a} - 2 - - - (1)$

to find:-

$\frac{ {a}^{2} }{ {b}^{2} } + \frac{ {b}^{2} }{ {a}^{2} }$

solution:-

rearrange equation 1

we get,

$\frac{a}{b} - \frac{b}{a} = - 2$

multiply -1 on both side.,

$\frac{b}{a} - \frac{a}{b} = 2$

squaring both the side.,

$( { \frac{b}{a} - \frac{a}{b} })^{2} = 4$

on expanding.,

$\frac{ {b}^{2} }{ {a}^{2} } + \frac{ {a}^{2} }{ {b}^{2} } - 2 \times \frac{b}{a} \times \frac{a}{b} = 4$

on simplification we get.,

$\frac{ {b}^{2} }{ {a}^{2} } + \frac{ {a}^{2} }{ {b}^{2} } = 4 + 2$

$\frac{ {a}^{2} }{ {b}^{2} } + \frac{ {b}^{2} }{ {a}^{2} } = 6$

hence find...

hope it helps you!!!!!!!!!!!!!