已知方程x²sinθ-2(sinθ+2)x+sinθ+12=o有两个不相等的实数根,求锐角θ的取值范围
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![已知方程x²sinθ-2(sinθ+2)x+sinθ+12=o有两个不相等的实数根,求锐角θ的取值范围](/uploads/image/z/8571025-1-5.jpg?t=%E5%B7%B2%E7%9F%A5%E6%96%B9%E7%A8%8Bx%26%23178%3Bsin%CE%B8-2%28sin%CE%B8%2B2%29x%2Bsin%CE%B8%2B12%3Do%E6%9C%89%E4%B8%A4%E4%B8%AA%E4%B8%8D%E7%9B%B8%E7%AD%89%E7%9A%84%E5%AE%9E%E6%95%B0%E6%A0%B9%2C%E6%B1%82%E9%94%90%E8%A7%92%CE%B8%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
已知方程x²sinθ-2(sinθ+2)x+sinθ+12=o有两个不相等的实数根,求锐角θ的取值范围
已知方程x²sinθ-2(sinθ+2)x+sinθ+12=o有两个不相等的实数根,求锐角θ的取值范围
已知方程x²sinθ-2(sinθ+2)x+sinθ+12=o有两个不相等的实数根,求锐角θ的取值范围
方程x²sinθ-2(sinθ+2)x+sinθ+12=o
有两个不相等的实数根,
∴Δ=4(sinθ+2)²-4sinθ(sinθ+12)>0
∴-8sinθ+4>0
∴sinθ
记t=sinθ
则方程为x^2t-2(t+2)+t+12=0
锐角时,2次项系数sinθ不为0
判别式大于0,即4(t+2)^2-4t(t+12)>0, 得:t<1/2, 得: 0<θ<π/6
故锐角θ的取值范围是(0,π/6)