# Hail Stewart-2!

Geometry Level 3

Let $$ABCD$$ be a square, and let $$E$$ and $$F$$ be points on $$AB$$ and $$BC,$$ respectively. The line through $$E$$ parallel to $$BC$$ and the line through $$F$$ parallel to $$AB$$ divide $$ABCD$$ into two squares and two non-square rectangles. The sum of the areas of the two squares is $$\frac{9}{10}$$ of the area of square $$ABCD.$$

Find $$\frac{AE}{EB}+\frac{EB}{AE}.$$

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