Problema Solution
Form the quadratic equation whose roots are the squares of the sum of the roots and squares of the difference of the roots of the equation 2x^2+2(m+n)x + m^2+n^2=0
Answer provided by our tutors
The roots of 2x^2+2(m+n)x + m^2+n^2=0 are X1 and X2
X1 + X2 = -(m+n)
X1*X2 = (m^2+n^2)/2
The two roots of new equation are X3 and X4
X3 = (X1+X2)^2
X4 = (X1-X2)^2
So
X3 + X4 = (X1+X2)^2 + (X1-X2)^2 = 2(X1^2 + X2^2) = 2[(m+n)^2 - m^2 -n^2]= 4mn
X3*X4 = (X1+X2)^2 * (X1-X2)^2 = (m+n)^2 * (-(m-n)^2) = -(m+n)^2 * (m-n)^2
So
the new equation is
x^2 -4mnx -(m+n)^2 * (m-n)^2 =0