作业帮已知x2+y2=2,求x2-2xy-y2的取值范围
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已知x2+y2=2,求x2-2xy-y2的取值范围
已知x2+y2=2,求x2-2xy-y2的取值范围
已知x2+y2=2,求x2-2xy-y2的取值范围
答：
x^2+y^2=2
设x=√2cost,y=√2sint
x^2-2xy-y^2
=2(cost)^2-4sintcost-2(sint)^2
=2cos2t-2sin2t
=2√2cos(2t+45°)∈[-2√2,2√2]
所以：取值范围是[-2√2,2√2]
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