实数x,y满足3x的平方+2y=6x 求x的平方+y的平方最大值最小值3x^2+2y^2=6x3x^2-6x+3+2y^2=33(x-1)^2+2y^2=3(x-1)^2+(2/3)y^2=1令x-1=sina y=√(3/2)cosax^2+y^2=(1+sina)^2+(3/2)(cosa)^2=(sina)^2+2sina+1+(cosa)^2+(1/2)[1-(sina)^2]=-(sina)^2/2
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实数x,y满足3x的平方+2y=6x 求x的平方+y的平方最大值最小值3x^2+2y^2=6x3x^2-6x+3+2y^2=33(x-1)^2+2y^2=3(x-1)^2+(2/3)y^2=1令x-1=sina y=√(3/2)cosax^2+y^2=(1+sina)^2+(3/2)(cosa)^2=(sina)^2+2sina+1+(cosa)^2+(1/2)[1-(sina)^2]=-(sina)^2/2
实数x,y满足3x的平方+2y=6x 求x的平方+y的平方最大值最小值
3x^2+2y^2=6x3x^2-6x+3+2y^2=33(x-1)^2+2y^2=3(x-1)^2+(2/3)y^2=1令x-1=sina y=√(3/2)cosax^2+y^2=(1+sina)^2+(3/2)(cosa)^2=(sina)^2+2sina+1+(cosa)^2+(1/2)[1-(sina)^2]=-(sina)^2/2+2sina+5/2=(-1/2)[(sina)^2-4sina-5]=(-1/2)(sina-2)^2+9/2当sina=-1时,x^2+y^2有最小值0当sina=1时,x^2+y^2有最大值4 y=√(3/2)cosax^2 这一步为什么是3/2
实数x,y满足3x的平方+2y=6x 求x的平方+y的平方最大值最小值3x^2+2y^2=6x3x^2-6x+3+2y^2=33(x-1)^2+2y^2=3(x-1)^2+(2/3)y^2=1令x-1=sina y=√(3/2)cosax^2+y^2=(1+sina)^2+(3/2)(cosa)^2=(sina)^2+2sina+1+(cosa)^2+(1/2)[1-(sina)^2]=-(sina)^2/2
整理得y=(-3x+6x)/2>=0,x(x-2)