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Solve: 4x2 + 4bx – (a2 – b2) = 0.
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
Difference =
=
=
Product =
=
using
=
using
2x[2x + (a + b)] - (a - b)[2x + (a + b)] = 0
[2x - (a - b)][2x + (a + b)] = 0
[2x - (a - b)] = 0 or [2x + (a + b)] = 0
2x = (a - b) or 2x = - (a + b)
Hence roots of equation are
Solve: