作业帮已知1
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 03:01:07
已知1
已知1
已知1
我们又见面了,我记得帮你解过一道题,再帮你做一道吧
1
x=asinb,y=acosb
1<=x^2+y^2<=2,1<=a^2<=2
x^2+xy+y^2
=a^2+a^2sinbcosb
=a^2[1+1/2*sin2b]
由于-1<=sin2b<=1
那么
1/2*1=0.5<=1/2a^2<=a^2[1+1/2*sin2b]<=3/2a^2<=3/2*2=3
即
0.5<=x^2+xy+y^2<=3
证毕
设x=a*cosb,y=a*sinb(a的平方在1和2之间)
x^2+xy+y^2=a^2+a^2*cosb*sinb
=a^2(1+sin2b/2)
0.5<=1+sin2b/2<=1.5
0.5<= 0.5a^2<=x^2+xy+y^2<=1.5a^2<=3