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