Question

`4x^2+4bx-(a^2-b^2)=0`

Answer 1

`4x^2+4bx-(a^2-b^2)=0` 

`4x^2+4bx=a^2-b^2` 

`(2x)^2+2xx2x  xxb+b^2=a^2-b^2+b^2=a^2-b^2+b^2`  (Adding `b^2` on both sides) 

`(2x+b)^2=a^2` 

`2x+b=+-a`                      (Taking square root on both sides) 

`2x+b=a  or  2x+b=-a` 

`2x=a-b  or  2x=-a-b` 

`x=(a-b)/2  or  x=-(a+b)/2` 

Hence, `(a-b)/2`  and `-(a+b)/2`  are the roots of the given equation.