Solve bu quadratic formula

Answer : Given : equation p²x² +(p²-q²)x - q² =0 

To find the solution of x using quadratic formulae

 

a = p²  , b=p²-q² ,c= - q² 

 

therefore x = [-b + (b²-4ac)^1/2 ]/2a ,[-b  - (b²-4ac)^1/2 ]/2a

 =[(p²-q²) + ((p²-q²)² - 4(p²)(-q²))^1/2] / 2p² and

 [(p²-q²) - ((p²-q²)² - 4(p²)(-q²))^1/2] / 2p²

 

as we know that (A+B)² =(A-B)² +4AB

=> (p²+q²)² = (p²-q²)² +4p²q²

 

=> x = ([(p²-q²) + ((p²+q²)²)^1/2] / 2p² and ([(p²-q²) - (p²+q²)²)^1/2] / 2p²

 

=> x =  [(p²-q²) + (p²+q²)] / 2p² and [(p²-q²) -(p²+q²)] / 2p²

=> x = q²/p² and -1 Answer