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

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Solve the following quadratic equation for x4x2  4a2x + (a4  b4) =0.

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Solution

We have

4x24a2x+(a4b4)=0

 (4x24a2x+a4)b4=0

[(2x)22(2x)(a)+(a2)2]b4=0

(2xa2)2(b2)2=0

(2xa2+b2)(2xa2b2)=0

2xa2+b2=0  or  2xa2b2=0

2x=a2b2  or  2x=a2+b2

`=>x=(a^2-b^2)/2 " or " x = (a^2+b^2)/2`

Concept: Solutions of Quadratic Equations by Factorization
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