若x²+y²-3y=0,求2x²-y²的取值范围

若x²+y²-3y=0,求2x²-y²的取值范围
若x²+y²-3y=0,求2x²-y²的取值范围

若x²+y²-3y=0,求2x²-y²的取值范围
x²>=0
所以x²=-y²+3y>=0
y(y-3)<=0
0<=y<=3
2x²-y²
=2(-y²+3y)-y²
=-3y²+6y
=-3(y-1)²+3
0<=y<=3
所以y=1,最大=3
y=3,最小=-9
所以-9≤2x²-y²≤3