Question

Solve the following quadratic equation for x :

9x² − 6b²x − (a⁴ − b⁴) = 0

Answer 1

For the given quadratic equation 9x²−6b²x−(a⁴−b⁴)=0, discriminant is calculated by 

D=(−6b²)²−4×9×[−(a4−b4)]

= 36b⁴+36(a⁴−b⁴)

=36a⁴

Using the quadratic formula, we get

`x=(6b^2+-sqrt(36a^4))/(2xx9)`

`= (6b^2+-6a^2)/18`

 `=(b^2+-a^2)/3`

`:. x=(b^2+a^2)/3" or "(b^2-a^2)/3`