MathDB

Let

ABCD

be a square, and let

E

and

F

be points on

\overline{AB}

and

\overline{BC}

, respectively. The line through

E

parallel to

\overline{BC}

and the line through

F

parallel to

\overline{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}

Problem Statement