Question

Solve the equation : 4x2 - 4a2 x + (a4 - b4) = 0.​

Answer 1

Answer:

x = ( a² + b² ) / 2  OR  x = ( a² - b² ) / 2

Step-by-step explanation:

Given :

4 x² - 4 a² x + ( a⁴ - b⁴ ) = 0

= > 4 x² - 4 a² x + a⁴ - b⁴  = 0

Rewrite as :

= > ( 2 x )² + ( a² )² - 2 . 2 x . a² - ( b )⁴ = 0

Using identity :

( a² + b² - 2 a b ) = ( a - b )²

= > ( 2 x - a² )² - ( b )⁴ = 0

= > ( 2 x - a² )² - ( b² )² = 0

Now using identity :

a² - b² = ( a + b ) ( a - b )

= > ( 2 x - a² + b² ) ( 2 x - a² - b² ) = 0

Value of x  as :

( 2 x - a² + b² ) = 0

2 x = a² - b²

x = ( a² - b² ) / 2

OR

( 2 x - a² - b² ) = 0

2 x = a² + b²

x = ( a² + b² ) / 2

Therefore we get value of x.