cosα=(2m^2-3)/(3-m) 求m的取值范围
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cosα=(2m^2-3)/(3-m) 求m的取值范围
∵cosα=(2m²-3)/(3-m),且-1≤m≤1,
∴-1≤(2m²-3)/(3-m)≤1.
对于 (2m²-3)/(3-m)≥ -1,
(2m²-3)/(m-3)≤1,
(2m²-3)/(m-3)-1≤0,
(2m²-m)/(m-3)≤0,
m(2m-1)(m-3)≤0,且m≠3,
得m≤0,或1/2≤m3;
∴-2≤m≤0,或1/2≤m≤3/2.
即m的取值范围是-2≤m≤0,或1/2≤m≤3/2.
首先由cosα的有界性得:
cosα=(2m²-3)/(3-m),且-1≤m≤1,
解得:-1≤(2m²-3)/(3-m)≤1.
然后情况一: (2m²-3)/(3-m)≥ -1,
有(2m²-3)/(m-3)≤1,
(2m²-3)/(m-3)-1≤0,
(2m²-m)/(m-3)≤0,
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首先由cosα的有界性得:
cosα=(2m²-3)/(3-m),且-1≤m≤1,
解得:-1≤(2m²-3)/(3-m)≤1.
然后情况一: (2m²-3)/(3-m)≥ -1,
有(2m²-3)/(m-3)≤1,
(2m²-3)/(m-3)-1≤0,
(2m²-m)/(m-3)≤0,
m(2m-1)(m-3)≤0,且m≠3,
解得m≤0,或1/2≤m<3;
情况二:(2m²-3)/(3-m)≤1
(2m²-3)/(m-3)≥ -1
(2m²-3)/(m-3)+1≥0
(2m²+m-6)/(m-3)≥0
(m+2)(2m-3)(m-3)≥0,且m≠3
解得-2≤m≤3/2,或m>3;
综上所述∴-2≤m≤0,或1/2≤m≤3/2.
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