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Question
`4x^2+4bx-(a^2-b^2)=0`
Solution
Sol:
We write, `4bx=2(a+b)x-2(a-b)x `as
`4x^2xx[-(a^2-b^2)]=-4(a^2-b^2)x^2=(a+b)x xx[-2(a-b)x]`
`∴ 4x^2+4bx-(a^2-b^2)=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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