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