x,y are the roots of the quadratic eq at2 +bt +c
x+y =-b/a 7 xy =c/a
now we have (x/y)2 + (y/x)2
= x4 +y4 /(xy)2
={(x2 +y2)2 - 2(xy)2 }/(xy)2 {x4 +y4 +2(xy)2} = (x2 +y2)2
={ ( (x+y)2 -2xy)2 -2(xy)2 )/(xy)2 {x2 +y2 +2xy) =(x+y)2
now substituting values of x+y and xy
{(b2 -2ac)2 -2(ac)2 }/(ac)2 this is the value of (x/y)2 + (y/x)2