26th Spanish Mathematical Olympiad Problems 1990

A1.  Show that √x + √y + √(xy) = √x + √(y + xy + 2y√x). Hence show that √3 + √(10 + 2√3) = √(5 + √22) + √(8 - √22 + 2√(15 - 3√22)). A2.  Every point of the plane is painted with one of three colors. Can we always find two points a distance 1 apart which are the same color?