已知实数x,y满足方程x^2+y^2-4x+1=0 (1) 求y-x的最大值和最小值; (2) 求x^2+y^2的最大值和最小值.

x^2+y^2-4x+1=0(x-2)^2+y^2=3令x-2=√3cosa ;y=√3sina(1)y-x=√3sina-√3cosa-2=√6sin(a-π/4)-2(y-x)max=√6-2(y-x)min=-√6-2(2)x^2+y^2=(2+√3cosa)^2+3sin²a=4+3cos²a+4√3cosa+3sin²a=7+4√3c...