Question

Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation 2x² + 2(p + q) x + p² + q² = 0 Solve the word problem

Answer 1

Answer:

x² - 4pqx - (p² - q²)² = 0

Step-by-step explanation:

2x² + 2(p + q) x + p² + q²= 0

Let say α & β  are roots

Then sum of roots

= α + β = - ( 2(p + q))/2 = - (p + q)

Product of Roots

= αβ  = (p² + q²)/2

Roots of Quadratic equation to be find

= (α + β)²  & ( (α - β)²

= (-(p + q))²  & (α + β)² - 4αβ

= (p + q)²   &  (p + q)²  - 2(p² + q²)

= (p + q)²   &  - (p² + q² - 2pq)

=  (p + q)²   & -(p-q)²

Quadratic equation is

(x -  (p + q)²)(x + ((p-q)²) = 0

=> x² + x( -4pq)  - (p² - q²)² = 0

=> x² - 4pqx - (p² - q²)² = 0