Here's an S.A.T. problem that stumped my students and me (for a little while).
a - b = 10
a2 - b2 = 50
My instincts were to look for a connection between (a - b)2 and a2 - b2, but it's really much simpler than that. Solve for a in terms of b in the first equation, and substitute into the second equation.
Edit: The original post contained a mistake. (10 + b)2 = 100 + 20b + b2, not 100 + 2b + b2.
Tuesday, April 29, 2008