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Question
Solve the following quadratic equation for x : 4x2 − 4a2x + (a4 − b4) =0.
Solution
We have
4x2−4a2x+(a4−b4)=0
⇒ (4x2−4a2x+a4)−b4=0
⇒[(2x)2−2(2x)(a)+(a2)2]−b4=0
⇒(2x−a2)2−(b2)2=0
⇒(2x−a2+b2)(2x−a2−b2)=0
⇒2x−a2+b2=0 or 2x−a2−b2=0
⇒2x=a2−b2 or 2x=a2+b2
`=>x=(a^2-b^2)/2 " or " x = (a^2+b^2)/2`
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