Question

please solve it ...need urgently​

Answer 1

let alpha=x,beta=y

x+y=p,. xy=q

x^2+y^2=(x+y)^2-2xy

=p^2-2q

x^4+y^4=(p^2-2q)^2-2q^2

=p^4+4q^2-4p^2q-2q^2

=p^4+2q^2-4p^2q

we have ,

x^2/y^2 + y^2/x^2 = x^4+y^4/(xy)^2

=p^4+2q^2-4p^2q/q^2

=p^4/q^2 -4p^2/q +2