1已知3(x-1)^2+2y^2=3,求x^2+y^2的最大值和最小值
问题描述:
1已知3(x-1)^2+2y^2=3,求x^2+y^2的最大值和最小值
答
(x-1)^2+(2/3)y^2=1令(x-1)^2=(sina)^2(2/3)y^2=(cosa)^2则y^2=(3/2)(cosa)^2x=1+|sina|或x=1-|sina|x^2=1+sina^2+2sina或x^2=1+sina^2-2sinax^2+y^2=(3/2)(cosa)^2+1+sina^2+2sina=(1/2)[1-(sina)^2]+2+2sina=-1/2(...