Question

Solve  `4x^2+4bx-(a^2-b^2)=0` 

Answer 1

`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.