Question

Find the roots of the equation
4 x2 + 4bx-(a2-b2) = 0 by the method of completing the square​

Answer 1

Answer:

4x2

Step-by-step explanation:

The given quadratic equation is 4x

2

−4ax+(a

2

−b

2

)=0

4x

2

−4ax+(a+b)(a−b)=0

⇒4x

2

+[−2a−2a+2b−2b]x+(a−b)(a+b)=0

⇒4x

2

+(2b−2a)x−(2a+2b)x+(a−b)(a+b)=0

⇒4x

2

+2(b−a)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)=0,2x−(a+b)=0

⇒x=

2

a+b

,

2

a−b

.