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Question
Solve the following quadratic equation for x:
x2 − 4ax − b2 + 4a2 = 0
Solution
The given quadratic equation is x2 − 4ax − b2 + 4a2 = 0
∴ x2 + (−4a)x − (4a2 + b2)= 0 [A = 1, B = −4a, C = 4a2 − b2]
`rArr x=(-(-4a)+-sqrt((-4a)^2-4xxlxx(4a^2-b^2)))/2` `[therefore x= (-B+-sqrtB^2-4AC)/(2A)]`
`rArr x=(4a+-sqrt(16^2-16a^2+4b^2))/2`
`rArr x=(4a+-sqrt4b^2)/2`
`rArr x=(4a+-2b)/2`
`rArr x=2a+-b`
`therefore x=2a+-b` `or` `x=2a-b`
Thus, the solution of the given quadratic equation is x = 2a + b or x = 2a − b.
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