Solve each of the following quadratic equations:

4x^{2} + 4bx - (a^{2} - b^{2}) = 0

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

Product = a.c

For the given equation a = 4 b = 4b c = - (a^{2} - b^{2})

= 4. - (a^{2} - b^{2})

= - 4a^{2} + 4b^{2}

And either of their sum or difference = b

= 4b

Thus the two terms are 2(a + b) and - 2(a - b)

Difference = 2a + 2b - 2a + 2b = 4b

Product = 2(a + b). - 2(a - b) = - 4(a^{2} - b^{2})

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

Hence the roots of equation are

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