Question

Solve the equation: 4x^2 - 4px + (p^2-q^2) = 0

Answer 1

Answer:

4x 2 −4px+p 2 −q 2 =0

⇒  x 2 −px+ 4 p 2 ​ − 4 q 2 ​ =0      

    [ Dividing both sides by 4 ]

Here, a=1,b=−p,c= 4 p 2 ​ − 4 q 2

​ ⇒  x 2 −px=− 4 p 2 ​ + 4 q 2 ​

Now, ( 2 b ​ ) 2 =( 2 −p ​ ) 2 = 4 p 2 ​

Now, we are adding 4 p 2 ​ on both side of equation.

⇒  x 2 −px+ 4 p 2 ​ =− 4 p 2 ​ + 4 q 2 ​ + 4 p 2 ​

⇒  (x− 2 p ​ ) 2 = 4 q 2 ​ ⇒  x− 2 p ​ =± 2 q

​ ∴  x= 2 q+p ​ and x= 2 −q+p ​

Explanation:

Answer 2

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