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Ecuación 13x+10=6x-4
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Expresiones idénticas
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Expresiones semejantes
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Expresiones con funciones
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4sin^3x+2sqrt(3)cos2x+sinx=2sqrt(3) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 ___ ___ 4*sin (x) + 2*\/ 3 *cos(2*x) + sin(x) = 2*\/ 3
$$\left(4 \sin^{3}{\left(x \right)} + 2 \sqrt{3} \cos{\left(2 x \right)}\right) + \sin{\left(x \right)} = 2 \sqrt{3}$$
Suma y producto de raíces
[src]
suma
/ ______________ \
/ / ______________ \ \ | / ___ / ___ ___\|
| | / ___ ___ ___| | |\/ -1 + 2*\/ 6 I*\\/ 2 - \/ 3 /| pi / 2 \ pi / 2 \
pi + I*\- log\- \/ -1 + 2*\/ 6 + I*\/ 3 - I*\/ 2 / + log(2)/ - I*log|----------------- - -----------------| + -- + I*log|--------------------------------| + -- + I*log|--------------------------------|
\ 2 2 / 2 | _____________| 2 | _____________|
| ___ ___ / ___ | | ___ ___ / ___ |
\\/ 2 + \/ 3 + \/ 1 + 2*\/ 6 / \\/ 2 + \/ 3 - \/ 1 + 2*\/ 6 /
$$\left(\left(\frac{\pi}{2} + i \log{\left(\frac{2}{\sqrt{2} + \sqrt{3} + \sqrt{1 + 2 \sqrt{6}}} \right)}\right) + \left(- i \log{\left(\frac{\sqrt{-1 + 2 \sqrt{6}}}{2} - \frac{i \left(- \sqrt{3} + \sqrt{2}\right)}{2} \right)} + \left(\pi + i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{-1 + 2 \sqrt{6}} - \sqrt{2} i + \sqrt{3} i \right)}\right)\right)\right)\right) + \left(\frac{\pi}{2} + i \log{\left(\frac{2}{- \sqrt{1 + 2 \sqrt{6}} + \sqrt{2} + \sqrt{3}} \right)}\right)$$
=
/ ______________ \
/ / ______________ \ \ | / ___ / ___ ___\|
| | / ___ ___ ___| | / 2 \ / 2 \ |\/ -1 + 2*\/ 6 I*\\/ 2 - \/ 3 /|
2*pi + I*\- log\- \/ -1 + 2*\/ 6 + I*\/ 3 - I*\/ 2 / + log(2)/ + I*log|--------------------------------| + I*log|--------------------------------| - I*log|----------------- - -----------------|
| _____________| | _____________| \ 2 2 /
| ___ ___ / ___ | | ___ ___ / ___ |
\\/ 2 + \/ 3 + \/ 1 + 2*\/ 6 / \\/ 2 + \/ 3 - \/ 1 + 2*\/ 6 /
$$- i \log{\left(\frac{\sqrt{-1 + 2 \sqrt{6}}}{2} - \frac{i \left(- \sqrt{3} + \sqrt{2}\right)}{2} \right)} + 2 \pi + i \log{\left(\frac{2}{\sqrt{2} + \sqrt{3} + \sqrt{1 + 2 \sqrt{6}}} \right)} + i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{-1 + 2 \sqrt{6}} - \sqrt{2} i + \sqrt{3} i \right)}\right) + i \log{\left(\frac{2}{- \sqrt{1 + 2 \sqrt{6}} + \sqrt{2} + \sqrt{3}} \right)}$$
producto
/ / ______________ \\
/ / ______________ \ \ | | / ___ / ___ ___\||
| | / ___ ___ ___| | | |\/ -1 + 2*\/ 6 I*\\/ 2 - \/ 3 /|| /pi / 2 \\ /pi / 2 \\
0*pi*I*\- log\- \/ -1 + 2*\/ 6 + I*\/ 3 - I*\/ 2 / + log(2)/*|-I*log|----------------- - -----------------||*|-- + I*log|--------------------------------||*|-- + I*log|--------------------------------||
\ \ 2 2 // |2 | _____________|| |2 | _____________||
| | ___ ___ / ___ || | | ___ ___ / ___ ||
\ \\/ 2 + \/ 3 + \/ 1 + 2*\/ 6 // \ \\/ 2 + \/ 3 - \/ 1 + 2*\/ 6 //
$$- i \log{\left(\frac{\sqrt{-1 + 2 \sqrt{6}}}{2} - \frac{i \left(- \sqrt{3} + \sqrt{2}\right)}{2} \right)} 0 \pi i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{-1 + 2 \sqrt{6}} - \sqrt{2} i + \sqrt{3} i \right)}\right) \left(\frac{\pi}{2} + i \log{\left(\frac{2}{\sqrt{2} + \sqrt{3} + \sqrt{1 + 2 \sqrt{6}}} \right)}\right) \left(\frac{\pi}{2} + i \log{\left(\frac{2}{- \sqrt{1 + 2 \sqrt{6}} + \sqrt{2} + \sqrt{3}} \right)}\right)$$
=
0
$$0$$
0
Respuesta rápida
[src]
x1 = 0
$$x_{1} = 0$$
x2 = pi
$$x_{2} = \pi$$
/ / ______________ \ \
| | / ___ ___ ___| |
x3 = I*\- log\- \/ -1 + 2*\/ 6 + I*\/ 3 - I*\/ 2 / + log(2)/
$$x_{3} = i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{-1 + 2 \sqrt{6}} - \sqrt{2} i + \sqrt{3} i \right)}\right)$$
/ ______________ \
| / ___ / ___ ___\|
|\/ -1 + 2*\/ 6 I*\\/ 2 - \/ 3 /|
x4 = -I*log|----------------- - -----------------|
\ 2 2 /
$$x_{4} = - i \log{\left(\frac{\sqrt{-1 + 2 \sqrt{6}}}{2} - \frac{i \left(- \sqrt{3} + \sqrt{2}\right)}{2} \right)}$$
pi / 2 \
x5 = -- + I*log|--------------------------------|
2 | _____________|
| ___ ___ / ___ |
\\/ 2 + \/ 3 + \/ 1 + 2*\/ 6 /
$$x_{5} = \frac{\pi}{2} + i \log{\left(\frac{2}{\sqrt{2} + \sqrt{3} + \sqrt{1 + 2 \sqrt{6}}} \right)}$$
pi / 2 \
x6 = -- + I*log|--------------------------------|
2 | _____________|
| ___ ___ / ___ |
\\/ 2 + \/ 3 - \/ 1 + 2*\/ 6 /
$$x_{6} = \frac{\pi}{2} + i \log{\left(\frac{2}{- \sqrt{1 + 2 \sqrt{6}} + \sqrt{2} + \sqrt{3}} \right)}$$
x6 = pi/2 + i*log(2/(-sqrt(1 + 2*sqrt(6)) + sqrt(2) + sqrt(3)))
Respuesta numérica
[src]
x1 = 65.9734457253857
x2 = 69.1150383789755
x3 = -21.9911485751286
x4 = 21.9911485751286
x5 = 81.8410042527195
x6 = -15.707963267949
x7 = 31.5755217952828
x8 = 9.42477796076938
x9 = 75.5578189455399
x10 = 100.690560174258
x11 = 97.3893722612836
x12 = 53.4070751110265
x13 = -87.8049990411293
x14 = 6.28318530717959
x15 = -34.5575191894877
x16 = 28.2743338823081
x17 = -56.3890725052314
x18 = -100.371369655488
x19 = -94.0881843483089
x20 = -12.4067753549743
x21 = -25.1327412287183
x22 = 153.9380400259
x23 = -131.946891450771
x24 = 257.770192853748
x25 = 59.6902604182061
x26 = -50.1058871980518
x27 = 56.5486677646163
x28 = 25.1327412287183
x29 = 78.3802210803599
x30 = 72.2566310325652
x31 = -50.2654824574367
x32 = -37.6991118430775
x33 = -43.9822971502571
x34 = 40.6811092372824
x35 = 47.1238898038469
x36 = -91.2657822134889
x37 = -414.690230273853
x38 = 3.14159265358979
x39 = -72.2566310325652
x40 = -81.6814089933346
x41 = 37.8587071024624
x42 = -40.8407044966673
x43 = -65.9734457253857
x44 = 0.0
x45 = -28.2743338823081
x46 = 91.106186954104
x47 = 43.9822971502571
x48 = -31.256331276513
x49 = 100.530964914873
x50 = -97.3893722612836
x51 = -75.398223686155
x52 = 34.3979239301028
x53 = -78.5398163397448
x54 = 50.2654824574367
x55 = 94.2477796076938
x56 = -84.8230016469244
x57 = -91.106186954104
x58 = -6.12359004779468
x59 = -103.672557568463
x60 = 88.1241895598991
x61 = -59.6902604182061
x62 = -9.58437322015429
x63 = 12.5663706143592
x64 = -69.1150383789755
x65 = -8695.76886987716
x66 = -53.5666703704114
x67 = -110.115338135028
x68 = 18.8495559215388
x69 = -47.2834850632318
x70 = 56.7082630240012
x71 = -62.8318530717959
x72 = -3480.72506491811
x73 = 15.707963267949
x74 = -18.8495559215388
x75 = -3.3011879129747
x76 = -97.5489675206685
x77 = 430.238598282417
x78 = 84.6634063875395
x79 = 62.8318530717959
x80 = -31.4159265358979
x80 = -31.4159265358979