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Question
Solve `4x^2+4bx-(a^2-b^2)=0`
Solution
`4x^2+4bx-(a^2-b^2)=0`
⇒ `4x^2+4bx-(a-b)(a+b)=0`
⇒`4x^2+2[(a+b)-(a-b)]x-(a-b)(a+b)=0`
⇒`4x^2+2(a+b)x-2(a-b)x-(a-b)(a+b)=0`
⇒`2x[2x+(a+b)]-(a-b)[2x+(a+b)]=0`
⇒`[2x+(a+b)][2x-(a-b)]=0`
⇒`2x+(a+b)=0 or 2x-(a-b)=0`
⇒` x=(-a+b)/2` or ` x=(a-b)/2`
Hence, `-(a+b)/2` and `(a-b)/2` are the roots of the given equation.
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