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