Question

find quadratic eqation such that its roots are square of sum of the roots and squareof difference of the roots of equation 2x²+2(p+q)x+p²+q²=0​

Answer 1

x² - 4pqx - (p² - q²)² = 0

Step-by-step explanation:

let say a and b are roots of given equation

2x²+2(p+q)x+p²+q²=0

then a + b = -2(p+q)/2 = -(p + q)

ab = (p²+q²)/2

square of sum of the roots = (a + b)²

= (-(p+q))²

= p² + q² + 2pq

= (p + q)²

square of difference of the roots = ( a - b)²

= (a + b)² - 4ab

= (-(p+q))² - 4(p² + q²)/2

= p² + q² + 2pq - 2p² - 2q²

= -(p² + q² - 2pq)

= - (p - q)²

(x - (p + q)²)(x + (p - q)²) = 0

x² - 4pqx - (p² - q²)² = 0

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