If p^2x^2-q^2=0 then x=?

1.	If p^2x^2-q^2=0 then x=?
Answer» Explanation: GIVEN quadratic equation is p²x² + ( p² - q² )X - q² = 0 dividing each term with p² , p²x² / p² + [ ( p² - q² ) / p² ] x - q² / p² = 0 ⇒ x² + [ 1 - q² / p² ] x - q² / p² = 0 To find the roots split the MIDDLE term ⇒ x² + x - ( q² / p² ) x - q² / p² = 0 ⇒ x ( x + 1 ) - ( q² / p² ) ( x + 1) = 0 ⇒ ( x+ 1 ) ( x - q² /p² ) = 0 Therefore, x+1 =0 or x - q² / p² =0 x= -1 or x = q² / p²

Answer»

Explanation:

GIVEN quadratic equation is

p²x² + ( p² - q² )X - q² = 0

dividing each term with p² ,

p²x² / p² + [ ( p² - q² ) / p² ] x - q² / p² = 0

⇒ x² + [ 1 - q² / p² ] x - q² / p² = 0

To find the roots split the MIDDLE term

⇒ x² + x - ( q² / p² ) x - q² / p² = 0

⇒ x ( x + 1 ) - ( q² / p² ) ( x + 1) = 0

⇒ ( x+ 1 ) ( x - q² /p² ) = 0

Therefore,

x+1 =0 or x - q² / p² =0

x= -1 or x = q² / p²

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