已知实数x,y满足xx+yy-2x=0,则2xx+yy的取值范围是

X^2+Y^2-2X=0
Y^2=2X-X^2

2X^2+Y^2
=2X^2+2X-X^2=2X+X^2=(X+1)^2-1
由于x^2-2x=-y^2<=0
x(x-2)<=0
0<=x<=2
所以当x=0时有最小值是0,当x=2时有最大值是8
故取值范围是[0,8]

≥0

xx+yy-2x=0,
yy=2x-xx
则2xx+yy=xx+2x