Question

x²-1/x²+1=4/5,Solve the given equation using the general formula.

Answer 1

$\frac{{x }^{2}+1 }{ {x}^{2} + 1 } = \frac{4}{5} \\ 5 {x}^{2} + 5 = 4 {x}^{2} + 4 \\ {x}^{2} = 4 - 5 \\ {x }^{2} = - 1 \\ x = \sqrt{1} \\ x = i$

Answer 2

Solution :

( x² - 1 )/( x² + 1 ) = 4/5

Do the cross multiplication ,

=> 5( x² - 1 ) = 4( x² + 1 )

=> 5x² - 5 = 4x² + 4

=> 5x² - 4x² -5 - 4 = 0

=> x² - 9 = 0

Compare this with ax² + bx + c = 0,

a = 1 , b = 0 , c = -9

Discreminant ( D ) = b² - 4ac

= 0² - 4 × 1 × ( -9 )

= 36

D = 36

************************************

We know the quadratic formula:

x = [ -b ± √D ]/2a

***********************************
Here ,

x = [ -0 ± √36 ]/( 2× 1 )

= ±√36/2

= ± 6/2

= ± 3

Therefore ,

x = -3 or x = 3

•••••