Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

x^{2} – 2ax + (a^{2} – b^{2}) = 0

Given: x^{2} – 2ax + (a^{2} – b^{2}) = 0

Comparing with standard quadratic equation Ax^{2} + Bx + C = 0

A = 1, B = – 2a, C = a^{2} – b^{2}

Discriminant D = B^{2} – 4AC

= (– 2a)^{2} – 4.1.(a^{2} – b^{2})

= 4a^{2} – 4a^{2} + 4 b^{2} = 4 b^{2} > 0

Hence the roots of equation are real.

Roots are given by

x = (a + b) or x = (a – b)

Hence the roots of equation are (a + b) or (a – b)

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