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问题: 不等式问题1

设实数x,y满足x^2+(y-1)^2=1,当x+y+c≥0时,c的取值范围是多少?

解答:

设x=cosa ,y =1+sina
x+y+c≥0
==>c≥ -x-y =-cosa-1-sina
=-√2[sin(a+π/4)-1
==> -√2-1≤c≤√2 -1