Give two or three examples to illustrate the necessity of establishing a mathematical model, including the background of practical problems, the purpose of modeling, and what kind of model is generally needed? 1. If the real number x.y satisfies the equation (x-3)? 0? 5+(y-3)？ 0? 5=6 to find the maximum and minimum value of y/x, which is actually to find the slope of the connecting line between the point on the circle and the origin, center (3,3) and radius √6. Let the slope of the point on the circle and the origin be k, then the linear equation is y=kx, that is, kx-y=0, and this straight line passes through the circle. Obviously, the distance from the center of the circle to the straight line should be less than or equal to the radius of the circle, using | 3k-3. 0? 5)≤√6, that is, (3k-3)? 0? 5/√( 1+k？ 0? 5)≤6，→(k？ 0? 5-4k- 1)/√( 1+k？ 0? 5)≤0，→k？ 0? 5-4k- 1≤0, and 2-√5≤k≤2+√5 is obtained. 2, known to meet a? 0? 5+b？ 0? 56=4, then (a-3)? 0? 5+(b-4)？ 0? What are the minimum and maximum values of 5? Is to find the distance from a point on a circle with the center of the circle as the origin and a radius of 2 to (3,4). Obviously, the longest point and the shortest point are both on the connecting line between the center of the circle and the point, so the maximum value is 7 and the minimum value is 3.3, and X is known. 0? 5+y？ 0? 5+z？ 0? 5= 1, x+y+z=√3, so I want to ask if x, y and z have any solutions. If so, please answer them. x？ 0? 5+y？ 0? 5+z？ 0? 5= 1 is a sphere with (0,0,0) as the center and 1 as the radius. X+y+z=√3 is the distance from the plane (0,0,0) where the intercept of x, y and z is √3 to x+y+z=√3 = | 0+0+0. 0? 5+ 1? 0? 5+ 1? 0? 5) = 1= >X+y+z=√3 is the tangent plane of the sphere = & gt(x, y, z) There is only one solution (tangent point) = & gt(x? 0? 5+y？ 0? 5+z？ 0? 5)*( 1? 0? 5+ 1? 0? 5+ 1? 0? 5)≥(x+y+z)？ 0? 5 equal sign holds =>x: y: z =1:1:1= > x = y = z =(√3)/3 = & gt； (x，y，z)=(√3/3，√3/3，√3/3) ...