Q. 554.5( 2 Votes )

x2 – 4ax + 4a2 – b2 = 0

Answer :

Using splitting middle term, the middle term of the general equation is divided in two such values that:

Product = a.c


For the given equation


= =


And either of their sum or difference = b


=


Thus the two terms are


Sum =


=


=


Product = using


= =






x[x-(2a + b)]-(2a-b)[x-(2a + b)] = 0


[x-(2a-b)][x-(2a + b)] = 0


[x-(2a-b)] = 0 or [x-(2a + b)] = 0


x = (2a-b) or x = (2a + b)


Hence roots of equation are x = (2a - b) or x = (2a + b)


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