Show that real numbers, p,q,r satisfy the condition p4(q−r)2+2p2(q+r)+1=p4 if and only if the quadratic equations x2+px+q=0 and y2−py+r=0 have real roots (not necessarily distinct) which can be labeled by x1,x2 and y1,y2, respectively, in such a way that x1y1−x2y2=1. algebrapolynomialquadraticsalgebra unsolved