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Question

Solve the following quadratic equations by factorization method: [4 MARKS]

4x24ax+(a2b2)=0

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Solution

Concept: 1 Mark
Application: 2 Marks
Answer: 1 Mark


We have,

4x24ax+(a2b2)=0

Here, Constant term =(a2b2)=(ab)(a+b)

and, the coefficient of middle term =4a

Also, Coefficient of the middle term 4a={2(a+b)+2(ab)}

4x24ax+(a2b2)=0

4x2{2(a+b)+2(ab)}x+(a+b)(ab)=0

4x22(a+b)x2(ab)x+(a+b)(ab)=0

{4x22(a+b)x}{2(ab)x(a+b)(ab)}=0

2x{2x(a+b)}(ab){2x(a+b)}=0

{2x(a+b)}{2x(ab)}=0

{2x(a+b)}=0 or, {2x(ab)}=0

2x=a+b or, 2x=abx=a+b2 or, x=ab2


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