If x and y are positive integers such that  xy+x+y = 71,  x2y +xy2 =880, then x 2+y2 is equal to

∵xy+x+y=71⇒xy+(x+y)=71and  x2y+xy2=880⇒ xy(x+y)=880⇒xy and (x+y) are the roots of the quadratic equation. t2−71t+880=0⇒(t−55)(t−16)=0⇒t=55,16x+y=16andxy=55So,x2+y2=(x+y)2−2xy=(16)2−110=146