SMO 2025 Junior (Problem 8)If xxx and yyy are positive integers such that xy−9x−9y=20xy - 9x - 9y = 20xy−9x−9y=20, find the value of x2+y2x^2 + y^2x2+y2.Related TopicsToolkit 23 — SFFT (Simon's Favorite Factoring Trick)Hints (3)Hint 1Use Identity 23: SFFT (Simon’s Favorite Factoring Trick).Hint 2(x−9)(y−9)=101(x-9)(y-9)=101(x−9)(y−9)=101Hint 3Since xxx and yyy are positive integers, w.l.o.g. x−9=1, y−9=101\text{w.l.o.g. } x-9=1,\ y-9=101w.l.o.g. x−9=1, y−9=101.Final Answer122001220012200