Question

a²b²x²+b²x-a²x-1=0 ( cbse 2005)

Answer 1

a²b² x² + b²x - a² x - 1 = 0

b² x( a²x + 1 ) - ( a² x + 1 ) = 0

( a² x + 1 ) ( b² x - 1 ) = 0

Therefore ,

a²x + 1 = 0 or b²x - 1 = 0

x = ( - 1 / a² ) or x = 1 / b²

I hope this helps you.

:)

Answer 2

Answer:

$\begin{lgathered}x = \frac{ -B \pm \sqrt{ {B}^{2} - 4 AC} }{2 A} \\ \\ \implies \: x = \frac{ - ( {b}^{2} - ac) \pm \sqrt{( {b}^{2} - ac {)}^{2} } - 4(ab) ( - bc) }{2ab} \\ \\ \implies \: x \: = \frac{ - ( {b}^{2} - ac) \pm \sqrt{( {b}^{2} - ac {) }^{2} +4a {b}^{2}c } }{2ab} \\ \\ \implies \: x = \frac{ - ( {b}^{2} - ac) \pm \sqrt{ {b}^{4} - 2a {b}^{2}c + {a}^{2} {c}^{2} + 4a {b}^{2}c } }{2ab} \\ \\ \implies \: x = \frac{ - ( {b}^{2} - ac) \pm \sqrt{( {b}^{2} + ac {)}^{2} } }{2ab} \: \: \: \implies \: x = \frac{ - ( {b}^{2} - ac) \pm( {b}^{2} + ac) }{2ab} \\ \\ \implies \: x = \frac{ - ( {b}^{2} - ac) + ( {b}^{2} + ac) }{2ab} \: \: \: \: or \: \: \: \: x = \frac{ - ( {b}^{2} -ac) - ( {b}^{2} + ac) }{2ab} \\ \\ \implies \: x = \frac{2ac}{2ab} \: \: \: \: \: \: or \: \: \: \: x = \frac{ - 2 {b}^{2} }{2ab} \: \: \: \: \: \implies \: x = \frac{c}{b} \: \: \: \: \: \: or \frac{ - b}{a}\end{lgathered} </p><p>$