Q. 474.3( 11 Votes )

Solve each of the following quadratic equations:

x2 - 4ax - b2 + 4a2 = 0

Answer :

x2 - 4ax - b2 + 4a2 = 0

x2 - 4ax – ((b)2 – (2a)2) = 0


{using a2 - b2 = (a + b)(a - b)}


x2 - (b + 2a)x + (b - 2a)x - (b + 2a)(b - 2a) = 0


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


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


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


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


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


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


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