证明 [tex=10.786x1.5]DgiTp2BzHSz0hdgYPbR44t6t5HrtCGd/nOGT2VdCgBI=[/tex]（[tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 为实数）的三个根是某三角形的内角的正弦，则 [tex=10.357x1.571]4Y3JrF0sJX7nG7X79wmIAGzY0ANJjmKi5EJEHdI887GXndu2aS1Rntl52axZX4Bq[/tex]
证 设 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 的根为 [tex=4.0x1.0]LPsc8hYEuA1nbYt0TU9lDouGJUrh/nJwlhKEyuB5Zo0=[/tex] 于是有 [tex=14.786x1.357]xGpMM3cpkr2lKxxC2kwGL/syL/WOJxQOUUnVLRwoSuUX3hVSiEPyNGTa3JQqGXwfuFcP8RKMlPz14/KQugv7ig==[/tex]，[tex=21.071x1.214]/8xz4VFP9IGpciq/tb20RHTQAlUK5AoW+La/ubSGgRnxZlzZZln9EiQ8p+ItnWXqXM+Kkd3mSpSQlwmpqmL3MZ6HAg6KYSvL1w3N/6X6QRDMAwIsvrOrHKeOzW6avQb8[/tex] 由此可见 [tex=23.643x1.5]spN4UuyaaV9jAdyYYKqjyIuOmpWxTyKX3aAwR7c8COon1Dw+mZzxHsRkgBUaylb6BmcxY/pQx9KccZCOQVlRDn6SIvOyalkbwBz835o5//0A0okv+jXXfsKHYQrWc6+X[/tex] 进一步有[tex=30.357x3.857]cxN5jx+JCm6iNhiPFI21o2V0pMErRFyxfI8olVaSMw2vTqQw+CWJ1QUzL71qzyPsRe0/AtuOdG+bBWE5WWhYvhUIPXpZe0tJffTj/+vOwCilHzukMTwyapWOFax7WwrMt6JE+nGCXg04b7gOmJOiA6bwr3BGF2YmZIkvs6VeXfMmANXSnguXd7HMNCPldkZpUcM6VqTR+kFpXwrCf7IZN/efIRXxGDpG6mjEYeD586wX6XQs9pEsQ+ksgVKd7W0t7US/uzwAv0LnTDv7pQvR5IbAS5RlAWaLiFsf1iyURjG9pI/d0ZFq33pnNdxGTrGz+hKehrc6kXnWW1vHN/72PWbsVggUQ1mbF7ypDlZfzoSmkeK3t2luU+vfSGhPXsN433Jat/TIzqO6urBiFybHJqIhxgV7NiqwjoJ3Be1kPgdSyb3i1fXEw+OaVk6H/hnY[/tex]于是[tex=31.929x10.214]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[/tex]设 [tex=15.5x2.143]n8rx4T1+2J7pF6TWbC7KxkQNUGcX7PMaVrc76Lg4TWQT46BtA3m4glwL9Yrx0ngktmhbi15laFVInFhzTjzBURWhpmNKQOfoNH9mpPzDsUk=[/tex] 因此 [tex=14.286x1.357]EQCJH60bHn5mmvSA1Amh95fL71e/GGmeb3pFY6JrafeJbpDDIchY9HV2xyG7RSqA61x5D+fymThJ5BZPNA7GSQ==[/tex].于是[p=align:center][tex=24.714x7.214]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[/tex][tex=30.071x2.143]/Obhb+BSAU5OMarNSy+HMJC3t5QQDaUZRg7UG3X284xiKZVIHvffdothcd3jijjCRTiTFO4W47PyCXs1Wf2gopRlV2Efa3CCIXB9ry+/vNlQxsTmKNq6LQ39jxTAaORKJXpNgVk1EZxZzoSsJYz75l0yQfuEsQVMVvf1aGaKJ2Ej+dKWXsCs0lfdqUP2CyUPCnRaNPSJflsRkA5OpSHJSLK2gmK7Ub1ShwNjnwmYnB4=[/tex]最后，得到[tex=30.929x3.071]g5VddJNjJX3TRIc4APAZ0VLN5+cKorzVcgL/7knsyl07WDPr0pVLtAGitHGfs07g/Dn1huK48ybQdH5+fugfPmDgpzqGKaBj7E+yG3r3+vm43MPqHPRP/V9G9Rl8yagcFigsAY6l2QzKJjtPBz172dFJbABb9mTEJ8p10z9G4VzboDOUgY8SvdYyHlCSIKLCldbfW8AXnIvErIvhGT5gJiFQ5qC43xPyTBgFiRvZKNB+nNqaSWxff6PCXmfllrhPorVAFYm5wtz1yokt3o+rDItSxnLdq9ZJKH0J3q/CcshgrgjkaUrTreUDDIrJftKKbWqdUYeTdEAadl1CNhAaFQ==[/tex]因而结论成立.
举一反三
- 证明 [tex=10.786x1.5]DgiTp2BzHSz0hdgYPbR44t6t5HrtCGd/nOGT2VdCgBI=[/tex]（[tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 为实数）的三个根的实部都是负数的充分必要条件是 [tex=10.286x1.214]P7P+Tzkvwa9Kd6HH8B8gaE5kbxWC7KZ2JTiC09SaKwE=[/tex]
- 采用基2时间抽取FFT算法流图计算8点序列的DFT，第一级的数据顺序为 A: x[0],x[2],x[4],x[6],x[1],x[3],x[5],x[7] B: x[0],x[1],x[2],x[3],x[4],x[5],x[6],x[7] C: x[0],x[4],x[2],x[6],x[1],x[5],x[3],x[7] D: x[0],x[2],x[1],x[3],x[4],x[6],x[5],x[7]
- 采用基2频率抽取FFT算法计算点序列的DFT,以下()流图是对的。 A: x[0]，x[1]，x[2]，x[3]，x[4]，x[5]，x[6]，x[7] B: x[0]，x[2]，x[4]，x[6]，x[1]，x[3]，x[5]，x[7] C: x[0]，x[2]，x[1]，x[3]，x[4]，x[6]，x[5]，x[7] D: x[0]，x[4]，x[2]，x[6]，x[1]，x[5]，x[3]，x[7]
- set1 = {x for x in range(10)} print(set1) 以上代码的运行结果为？ A: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} C: {1, 2, 3, 4, 5, 6, 7, 8, 9} D: {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
- 关于齐次线性方程组[tex=8.929x5.214]fnpmC2J6JmQBLyo5NmGAz3pxIWlZT4lLIQGYQSD4ipO+84/TKQgCBAiWddrI/A2JTCrW6CMDML/UCBwu/wBMtshof+xJ4K6heMqCeaAG3RtcN0VbFY7EaRL/Sr1aCChfgQKEzbwOszTjrFLy47OWzJrJk44EHsf18otMzPyHMzUdyVUl9wLjEhj3K1SBEQaP[/tex][tex=2.714x1.357]sfA/TcgqbJX3o+/kkEKJyw==[/tex]为实数 ), 解的下列四种结论：(1) 当 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 全为零时，仅有令解(2) 当 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex]全为零时，有非零解(3) 当 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex]不全为零时，仅有零解(4) 当 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 全不为零时，有非零解判断正确的选项是 A: (1), (3) 正确 B: (2), (3) 正确 C: (2), (4) 正确 D: (2), (3), (4) 正确
内容
- 0
下列哪条语句是正确的（ ） A: A=[1 2;3 4];B=[3;7];A.*B; B: A=cell(2,3);A(1,2)=[4;5]; C: A=[2 3 5 7;9 4 6 1;7 3 2 5];B=[1 7;0 5];A(2:end,2:2:end) D: x=-5:5;y=-5:5;z=x.*x-y.*y;surf(x,y,z);
- 1
>>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']
- 2
设X，Y为两个随机变量，且P{X ³0，Y ³ 0} = 3/7 , P{X ³ 0} = P{ Y ³ 0} = 4/7 ,则P{max(X, Y) ³ 0} = ( )． A: 1/7 B: 3/7 C: 4/7 D: 5/7
- 3
有代码片段：function f(y) {var x=y*y;return x;} for(var x=0;x< 5;x++) {y=f(x);document.writeln(y);}输出结果是( )。 A: 0 1 2 3 4 B: 0 1 4 9 16 C: 0 1 4 9 16 25 D: 0 1 2 3 4 5
- 4
假设x=4,y=2,m=5,n=4,w=12,t=9，则经过表达式（w=x 0 9