If α≠β and α2=5α−3,β2=5β−3, then the equation whose roots are αβ and βα is

α,β are roots of x2=5x−3 or x2−5x+3=0. Thus,α+β=5,αβ=3 Next,          αβ+βα=α2+β2αβ=(α+β)2αβ−2                                =253−2=193and               αββα=1Thus, the quadratic equation whose roots are  αβ,βα isx2−193x+1=0 or 3x2−19x+3=0