若不等式a大于等于-X^2-Y^2-2X-2Y,则实数a的取值范围是
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若不等式a大于等于-X^2-Y^2-2X-2Y,则实数a的取值范围是
若不等式a大于等于-X^2-Y^2-2X-2Y,则实数a的取值范围是
若不等式a大于等于-X^2-Y^2-2X-2Y,则实数a的取值范围是
a≥-x²-y²-2x-2y=2-(x²+2x+1+y²+2y+1)=2-[(x+1)²+(y+1)²]
(x+1)²+(y+1)²≥0 恒成立,则2-[(x+1)²+(y+1)²]≤2
为使 a≥-x²-y²-2x-2y,a的取值范围应该是[2,+∞)
-X^2-Y^2-2X-2Y=-(x^2+2x+1)-(y^2+2y+1)+2
=-(x+1)^2-(y+1)^2+2<=2
a>=-X^2-Y^2-2X-2Y
所以a>=2
x^2+2x+a>=-y^2-2 =>(x+1)^2+y^2>=-(a+2) 由题知此式对一切实数x,y都成立又(x+1)^2+y^2>=0 所以-(a+2)<=0 a>=-2 ..