设实数x,y满足x^2+(y-1)^2=1,若对满足x,y,不等式x+y+c≥0恒成立 ,则c的取值范围
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设实数x,y满足x^2+(y-1)^2=1,若对满足x,y,不等式x+y+c≥0恒成立,则c的取值范围设实数x,y满足x^2+(y-1)^2=1,若对满足x,y,不等式x+y+c≥0恒成立,则c的取值
设实数x,y满足x^2+(y-1)^2=1,若对满足x,y,不等式x+y+c≥0恒成立 ,则c的取值范围
设实数x,y满足x^2+(y-1)^2=1,若对满足x,y,不等式x+y+c≥0恒成立 ,则c的取值范围
设实数x,y满足x^2+(y-1)^2=1,若对满足x,y,不等式x+y+c≥0恒成立 ,则c的取值范围
x=cosa y=1+sina
x+y=cosa+1+sina=1+根2sin(a+派/4)
x+y的最小值为1-根2
x+y≥-c
1-根2≥-c
c≥根2-1
换句话即x+y的取值范围设x+y=t x=t-y
t*t-2ty+y*y+y*y-2y+1=1
即2y*y-(2t+2)y+t*t=0
判别式》=0解出1-根号2《=t《=1+根号2
x+y+c≥0 c》=-(x+y) c>=(根号2)-1
由柯西不等式,(x+y-1)^2<=2[(x^2+(y-1)^2]=2
x+y-1>=-√2
x+y>=1-√2
因为x+y>=-c恒成立,故-c<=1-√2,即c>=√2-1
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