Q. 84.0( 20 Votes )

Solve the equatio

Answer :

Given: equation 4x2 – 4a2x + (a4-b4) =0


To find: The roots by factorisation method


Method Used:


To solve the quadratic equation by factorisation method, follow the steps:


1) Multiply the coefficient of x2 and constant term.


2) factorise the result obtained in step 1.


3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them


You get coefficient of x.


Explanation:


Here,


Coefficient of x2 = 4


Constant term = (a4-b4)


As a2-b2 = (a-b) (a +b)


(a4-b4) = (a2 – b2) (a2+b2)


As 4(a4-b4) = 4[(a2 – b2) (a2+b2)]


Coefficient of x = - 4a2


=- 2a2 - 2a2


Add and subtract 2b2 to get,


= -2a2 - 2a2 + 2b2 - 2b2


= -2a2 – 2b2 – 2a2 + 2b2


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


4x2 – 4a2x + (a4-b4) = 0


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


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


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


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


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


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



Hence roots are .


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