This problem is a synthesis problem of functions. The key to solving this problem is to understand the quadratic equation of one variable, the properties of squares, the judgment and properties of congruent triangles, an analytic function and the judgment and properties of an isosceles right triangle by using the method of undetermined coefficients, and to construct congruent triangles as an auxiliary line.

The first question, the length of OA and OB can be obtained by solving the quadratic equation of one variable, and by passing through point D, making DE perpendicular to point E, according to the properties of the square.

Ad = ab', the detailed answer is here. As shown in the figure, in the plane rectangular coordinate system, the vertex A of the square ABCD is on the positive semi-axis of the Y axis, and the vertex B is on the positive semi-axis of the X axis. The lengths of OA > and OB are two of the quadratic equations X 2-7x+ 12 = 0. OB)。

(1) Find the coordinates of point D. 。

(2) Find the analytical formula of BC line.

(3) Is there a point P on the straight line BC that makes the triangle PCD an isosceles triangle? If it exists, please write down the coordinates of this point directly; If it does not exist, explain why.