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Solve` X^2-4ax+4a^2-b^2=0` - Mathematics

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Solve` x^2-4ax+4a^2-b^2=0` 

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Solution

`x^2-4ax+4a^2-b^2=0`  

⇒`x^2-4ax+(2a+b) (2a-b)=0` 

⇒`x^2-[(2a+b)+(2a-b)]x+(2a+b) (2a-b)=0` 

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

⇒`x[x-(2a+b)]-(2a-b)[x-(2a+b)=0]` 

⇒`[x-(2a+b)][x-(2a-b)]=0` 

⇒`x-(2a+b)=0  or  x-(2a-b)=0` 

⇒`x=(2a+b)  or  x=(2a-b)` 

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

Concept: Application of Quadratic Equation
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 10 Quadratic Equations
Q 55

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