实数x,y满足x2+y2=4(y≥0),试求m=(根号3)x+y的取值范围
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实数x,y满足x2+y2=4(y≥0),试求m=(根号3)x+y的取值范围
![实数x,y满足x2+y2=4(y≥0),试求m=(根号3)x+y的取值范围](/uploads/image/z/8026571-11-1.jpg?t=%E5%AE%9E%E6%95%B0x%2Cy%E6%BB%A1%E8%B6%B3x2%2By2%3D4%28y%E2%89%A50%29%2C%E8%AF%95%E6%B1%82m%3D%EF%BC%88%E6%A0%B9%E5%8F%B73%EF%BC%89x%2By%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
相当于求直线y=-√3x+m与圆x^2+y^2=4有公共点时m的取值范围
将y=-√3x+m代入x^2+y^2=4得:
x^2+(-√3x+m)^2=4
4x^2-2√3mx+m^2-4=0
判别式=(-2√3m)^2-4*4*(m^2-4)≥0
12m^2-16m^2+64≥0
4m^2≤64
m^2≤16
-4≤m≤4
将y=-√3x+m代入x^2+y^2=4得:
x^2+(-√3x+m)^2=4
4x^2-2√3mx+m^2-4=0
判别式=(-2√3m)^2-4*4*(m^2-4)≥0
12m^2-16m^2+64≥0
4m^2≤64
m^2≤16
-4≤m≤4
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