5cos^2 α +4cos^2 β =4cosα,求cos^2 α +cos^2 β的取值范围?

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5cos^2 α +4cos^2 β =4cosα,求cos^2 α +cos^2 β的取值范围?

5cos^2 α +4cos^2 β =4cosα,求cos^2 α +cos^2 β的取值范围?
5cos^2 α +4cos^2 β =4cosα,求cos^2 α +cos^2 β的取值范围?

5cos^2 α +4cos^2 β =4cosα,求cos^2 α +cos^2 β的取值范围?
5(cosa)^2 +4(cosb)^2=4cosa
4(cosb)^2=4cosa-5(cosa)^2
-4<=4cosa-5(cosa)^2<=4
cosa=x
-1<=x<=1
-4<=4x-5xx<=4
(1/5)(2-2√6)<=x<=1
y=(cosa)^2+(cosb)^2
4y=4(cosa)^2+4(cosb)^2
=4(cosa)^2+4cosa-5(cosa)^2
=4cosa-(cosa)^2
=4x-xx
=4-(x-2)^2
(1/5)(2-2√6)<=x<=1
1-(1/4)((1/5)(2-2√6)-2)^2<=y<=3/4