1 Knowledge of circles. Draw a graph, where x 2+y 2-4x+ 1 = 0, (2,0) is the center of the circle. In y-x, when the straight line is tangent to the circle, the value of y-x is obtained, and its maximum value is 2; The minimum value is -2,

The value of x 2+y 2 is the same as the algorithm, so draw a graph. Let X 2+Y 2 = K, when this circle contains X 2+Y 2- 4x+ 1 = 0, the maximum value is 2+ root number 3, and the minimum value is 2- root number 3.

2y = √1-x 2 is an upper semicircle with the center of the circle as the origin, and the straight line y=x+b intersects with it at two different points, thus drawing a figure: 1 =