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cos(2x)-cos(x)²-√2×sin(x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
              2        ___           
cos(2*x) - cos (x) - \/ 2 *sin(x) = 0
$$\left(- \cos^{2}{\left(x \right)} + \cos{\left(2 x \right)}\right) - \sqrt{2} \sin{\left(x \right)} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
       pi        /       ___\     pi        /      ___\
pi + - -- - I*log\-1 + \/ 2 / + - -- - I*log\1 + \/ 2 /
       2                          2                    
$$\left(- \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}\right) + \left(\pi + \left(- \frac{\pi}{2} - i \log{\left(-1 + \sqrt{2} \right)}\right)\right)$$
=
       /      ___\        /       ___\
- I*log\1 + \/ 2 / - I*log\-1 + \/ 2 /
$$- i \log{\left(1 + \sqrt{2} \right)} - i \log{\left(-1 + \sqrt{2} \right)}$$
producto
     /  pi        /       ___\\ /  pi        /      ___\\
0*pi*|- -- - I*log\-1 + \/ 2 /|*|- -- - I*log\1 + \/ 2 /|
     \  2                     / \  2                    /
$$0 \pi \left(- \frac{\pi}{2} - i \log{\left(-1 + \sqrt{2} \right)}\right) \left(- \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}\right)$$
=
0
$$0$$
0
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
x2 = pi
$$x_{2} = \pi$$
       pi        /       ___\
x3 = - -- - I*log\-1 + \/ 2 /
       2                     
$$x_{3} = - \frac{\pi}{2} - i \log{\left(-1 + \sqrt{2} \right)}$$
       pi        /      ___\
x4 = - -- - I*log\1 + \/ 2 /
       2                    
$$x_{4} = - \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}$$
x4 = -pi/2 - i*log(1 + sqrt(2))
Respuesta numérica [src]
x1 = 31.4159265358979
x2 = 3.14159265358979
x3 = -47.1238898038469
x4 = -12.5663706143592
x5 = -69.1150383789755
x6 = 75.398223686155
x7 = -50.2654824574367
x8 = -65.9734457253857
x9 = -56.5486677646163
x10 = 59.6902604182061
x11 = 72.2566310325652
x12 = 91.106186954104
x13 = -91.106186954104
x14 = -62.8318530717959
x15 = -2789.73427638774
x16 = -6.28318530717959
x17 = 6.28318530717959
x18 = 62.8318530717959
x19 = 122.522113490002
x20 = 94.2477796076938
x21 = -9.42477796076938
x22 = -1259.77865408951
x23 = -37.6991118430775
x24 = 65.9734457253857
x25 = -100.530964914873
x26 = -43.9822971502571
x27 = 25.1327412287183
x28 = 21.9911485751286
x29 = 87.9645943005142
x30 = -571.769862953342
x31 = -40.8407044966673
x32 = -301.59289474462
x33 = -97.3893722612836
x34 = 43.9822971502571
x35 = -53.4070751110265
x36 = -31.4159265358979
x37 = 100.530964914873
x38 = -94.2477796076938
x39 = 78.5398163397448
x40 = 185.353966561798
x41 = -18.8495559215388
x42 = 47.1238898038469
x43 = 12.5663706143592
x44 = 81.6814089933346
x45 = 34.5575191894877
x46 = -75.398223686155
x47 = -15.707963267949
x48 = 50.2654824574367
x49 = -81.6814089933346
x50 = -3.14159265358979
x51 = -59.6902604182061
x52 = -501806.594557898
x53 = -28.2743338823081
x54 = -87.9645943005142
x55 = 9.42477796076938
x56 = -21.9911485751286
x57 = 56.5486677646163
x58 = 15.707963267949
x59 = 84.8230016469244
x60 = -78.5398163397448
x61 = 37.6991118430775
x62 = -72.2566310325652
x63 = -84.8230016469244
x64 = 69.1150383789755
x65 = 0.0
x66 = 28.2743338823081
x67 = 40.8407044966673
x67 = 40.8407044966673