Question

5. Solve the following quadratic equation by applying the quadratic formula:p^2x^2+(p^2-q^2)-q^2

Answer 1

p²x²+(p²-q²)-q²

=> a = p²

b = p²-q²

c = -q²

Now ,

We have to find D

where

D = b²-4ac

D = (p²-q²)² + 4 p²q²

= p⁴ + q⁴ - 2p²q² + 4p²q²

= p⁴ + q⁴ + 2p²q²


By using identity

a² + b² + 2ab = ( a + b )²

Here,

p⁴ + q⁴ + 2p²q² = ( p² + q² )²

So,

D = ( p² + q² )²


Now ,

=> x = ( - b ± √D )/2a

So,

x = [-( p² - q² ) ± √ ( p²+q²) ² ] / 2p²

x = {-p²+q² ± (p²+q² ) } / 2p²





⭐x = { -p² + q² + p² + q² } /2p²

x = 2q²/2p²

x = q²/p²


⭐ x = { -p² + q² -p²- q²}\2p²

x = -2p²/2p²

x = -2


@Altaf