Answer :

On factorizing the above equation,

(a4 – b4) = [(a2 + b2) (a2 – b2)]


The above relation is same as (a + b) (a – b) = a2 – b2


Here a = (a2 + b2) and b = (a2 - b2)


4x2 – 4a2x + (a4 – b4) = 0


4x2 – [2(a2 + b2) + 2(a2 – b2)] x + [(a2 + b2) (a2 – b2)] = 0


4x2 – 2x(a2 + b2) – 2x(a2 – b2) + [(a2 + b2) (a2 – b2)] = 0


2x[2x - (a2 + b2)] - (a2 - b2) [2x - (a2 + b2)] = 0


[2x - (a2 - b2)] [2x - (a2 + b2)] = 0


Solving the first part,


[2x - (a2 - b2)] = 0


2x = (a2 - b2)


x = (a2 - b2) / 2


Solving the second part,


[2x - (a2 + b2)] = 0


2x = (a2 + b2)


x = (a2 + b2) / 2


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