若2sin^2x+sin^2y=3sinx,则sin^2x+sin^2y的取值范围是

题目

若2sin^2x+sin^2y=3sinx,则sin^2x+sin^2y的取值范围是

答案

2sin^2x+sin^2y=3sinx
sin^2y=-2sin^2x+3sinx代入sin^2x+sin^2y
∴
sin^2x+sin^2y
=sin^2x-2sin^2x+3sinx
=-sin^2x+3sinx
=-(sin^2x-3sinx+9/4)+9/4
=-(sinx-3/2)^2+9/4
最大值=-(1-3/2)^2+9/4=2
最小值=-(-1-3/2)^2+9/4=-4
取值范围是[-4,2]
如果本题有什么不明白可以追问,如果满意记得采纳
如果有其他问题请另发或点击向我求助,答题不易,请谅解,谢谢.
祝学习进步!