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Solve the following quadratic equation for x : 9x^2 − 6b^2x − (a^4 − b^4) = 0 - Mathematics

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Solve the following quadratic equation for x :

9x2 − 6b2x − (a4b4) = 0

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Solution

For the given quadratic equation 9x26b2x(a4b4)=0, discriminant is calculated by 

D=(6b2)24×9×[(a4b4)]

= 36b4+36(a4b4)

=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`

Concept: Nature of Roots
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