Find quadratic equation such that its roots are square of sum of the roots asquare of difference of the roots of equation 2r +2(p + q)x p 0

Find quadratic equation such that its roots are square of sum of the r

1.	Find quadratic equation such that its roots are square of sum of the roots asquare of difference of the roots of equation 2r +2(p + q)x p 0
Answer» the roots of the required quation be M and N let the roots of the equation 2x²+2(p+q)x+p²+q²=0 be a and ba + b = -(p+q)ab = (p^2 + q^2) / 2(a+b)^2 = (p+q)^2(a-b)^2 = (a+b)^2 - 4ab(a-b)^2 = -(p - q)^2we wanted the values of square of sum of the roots and square of difference of the rootsNow M = (a+b)^2 = (p+q)^2 and N = (a-b)^2 = -(p - q)^2M + N = 4pqMN = (p+q)^2 [-(p - q)^2]MN= -(p^2 - q^2)^2hence the required equation isx^2 - (4pq)x - (p^2 - q^2)^2 = 0