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f(x) = g(x), -(sinx)^2 - cosx + 3 = mcosx
(cosx)^2 -1 - (1+m)cosx + 3 = 0
(cosx)^2 - (1+m)cosx + 2 = 0
cosx = (1/2) [(1+m) ± √(m^2+2m-7)]
则 m^2+2m-7 ≥ 0, m ≤ -1-2√2 或 m ≥ -1+2√2
另要满足 -2 ≤ (1+m) ± √(m^2+2m-7) ≤ 2
m ≥ 2√2 - 1 时,(1+m) + √(m^2+2m-7) ≥ 2√2, cosx ≥ 2√2 无解;
要满足 -2 ≤ (1+m) - √(m^2+2m-7) ≤ 2, -3-m ≤ -√(m^2+2m-7) ≤ 1-m,
-1+m ≤ √(m^2+2m-7) ≤ 3+m, 1-2m+m^2 ≤ m^2+2m-7 ≤ 9+6m+m^2,
1-2m ≤ 2m-7 ≤ 9+6m, m ≥ 2 , 综合 m ≥ 2。
m ≤ -1-2√2 时,(1+m) - √(m^2+2m-7) ≤ -2√2, cosx ≤ -2√2 无解;
要满足 -2 ≤ (1+m) + √(m^2+2m-7) ≤ 2,-3-m ≤ √(m^2+2m-7) ≤ 1-m,
9+6m+m^2 ≤ m^2+2m-7 ≤ 1-2m+m^2,
9+6m ≤ 2m-7 ≤ 1-2m , m ≤ -4 , 综合 m ≤ -4。
则 m ≤ -4 或 m ≥ 2。
(cosx)^2 -1 - (1+m)cosx + 3 = 0
(cosx)^2 - (1+m)cosx + 2 = 0
cosx = (1/2) [(1+m) ± √(m^2+2m-7)]
则 m^2+2m-7 ≥ 0, m ≤ -1-2√2 或 m ≥ -1+2√2
另要满足 -2 ≤ (1+m) ± √(m^2+2m-7) ≤ 2
m ≥ 2√2 - 1 时,(1+m) + √(m^2+2m-7) ≥ 2√2, cosx ≥ 2√2 无解;
要满足 -2 ≤ (1+m) - √(m^2+2m-7) ≤ 2, -3-m ≤ -√(m^2+2m-7) ≤ 1-m,
-1+m ≤ √(m^2+2m-7) ≤ 3+m, 1-2m+m^2 ≤ m^2+2m-7 ≤ 9+6m+m^2,
1-2m ≤ 2m-7 ≤ 9+6m, m ≥ 2 , 综合 m ≥ 2。
m ≤ -1-2√2 时,(1+m) - √(m^2+2m-7) ≤ -2√2, cosx ≤ -2√2 无解;
要满足 -2 ≤ (1+m) + √(m^2+2m-7) ≤ 2,-3-m ≤ √(m^2+2m-7) ≤ 1-m,
9+6m+m^2 ≤ m^2+2m-7 ≤ 1-2m+m^2,
9+6m ≤ 2m-7 ≤ 1-2m , m ≤ -4 , 综合 m ≤ -4。
则 m ≤ -4 或 m ≥ 2。
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