If 4x2−4ax+(a2−b2)=0 and (a,b∈R), then vaue of x is equal to
A
a+b2,a−b2
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B
2
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C
(a+b)2
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D
None of these
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Solution
The correct option is Aa+b2,a−b2 Given equation is:
4x2−4ax+(a2−b2)=0 ⇒4x2−{2(a+b)x+2(a−b)x}+a2−b2=0 ⇒{4x2−2(a+b)x}{2(a−b)x−(a2−b2)}=0 ⇒2x{2x−(a+b)}{2x−(a−b)}=0 ⇒2x−(a+b)=0 or 2x−(a−b)=0 ⇒x=a+b2 or x=a−b2 Hence, x=a+b2,a−b2 are required solutions.