Question

Solve the following quadratic equation for x:

x² − 4ax − b² + 4a² = 0

Answer 1

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.