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sin^4x+cos^4x+cos2x=0.5 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   4         4                    
sin (x) + cos (x) + cos(2*x) = 1/2
$$\left(\sin^{4}{\left(x \right)} + \cos^{4}{\left(x \right)}\right) + \cos{\left(2 x \right)} = \frac{1}{2}$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                                      /      ___\               /      ___\             /      ___\             /      ___\
  3*pi   pi   pi   3*pi     pi   I*log\2 - \/ 3 /     pi   I*log\2 + \/ 3 /   pi   I*log\2 - \/ 3 /   pi   I*log\2 + \/ 3 /
- ---- - -- + -- + ---- + - -- - ---------------- + - -- - ---------------- + -- - ---------------- + -- - ----------------
   4     4    4     4       2           2             2           2           2           2           2           2
$$\left(\frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right) + \left(\left(\left(- \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right) + \left(\left(\left(\left(- \frac{3 \pi}{4} - \frac{\pi}{4}\right) + \frac{\pi}{4}\right) + \frac{3 \pi}{4}\right) + \left(- \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right)\right)\right) + \left(\frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right)\right)$$ 
=
       /      ___\        /      ___\
- I*log\2 + \/ 3 / - I*log\2 - \/ 3 /
$$- i \log{\left(\sqrt{3} + 2 \right)} - i \log{\left(2 - \sqrt{3} \right)}$$ 
producto
                   /            /      ___\\ /            /      ___\\ /          /      ___\\ /          /      ___\\
-3*pi -pi  pi 3*pi |  pi   I*log\2 - \/ 3 /| |  pi   I*log\2 + \/ 3 /| |pi   I*log\2 - \/ 3 /| |pi   I*log\2 + \/ 3 /|
-----*----*--*----*|- -- - ----------------|*|- -- - ----------------|*|-- - ----------------|*|-- - ----------------|
  4    4   4   4   \  2           2        / \  2           2        / \2           2        / \2           2        /
$$\frac{3 \pi}{4} \frac{\pi}{4} \cdot - \frac{3 \pi}{4} \left(- \frac{\pi}{4}\right) \left(- \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right) \left(- \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right) \left(\frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right) \left(\frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right)$$ 
=
    4 /          /      ___\\ /          /      ___\\ /          /      ___\\ /          /      ___\\
9*pi *\pi + I*log\2 + \/ 3 //*\pi + I*log\2 - \/ 3 //*\pi - I*log\2 + \/ 3 //*\pi - I*log\2 - \/ 3 //
-----------------------------------------------------------------------------------------------------
                                                 4096
$$\frac{9 \pi^{4} \left(\pi - i \log{\left(2 - \sqrt{3} \right)}\right) \left(\pi + i \log{\left(2 - \sqrt{3} \right)}\right) \left(\pi - i \log{\left(\sqrt{3} + 2 \right)}\right) \left(\pi + i \log{\left(\sqrt{3} + 2 \right)}\right)}{4096}$$ 
9*pi^4*(pi + i*log(2 + sqrt(3)))*(pi + i*log(2 - sqrt(3)))*(pi - i*log(2 + sqrt(3)))*(pi - i*log(2 - sqrt(3)))/4096
Respuesta rápida [src] 
     -3*pi
x1 = -----
       4
$$x_{1} = - \frac{3 \pi}{4}$$ 
     -pi 
x2 = ----
      4
$$x_{2} = - \frac{\pi}{4}$$ 
     pi
x3 = --
     4
$$x_{3} = \frac{\pi}{4}$$ 
     3*pi
x4 = ----
      4
$$x_{4} = \frac{3 \pi}{4}$$ 
                 /      ___\
       pi   I*log\2 - \/ 3 /
x5 = - -- - ----------------
       2           2
$$x_{5} = - \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}$$ 
                 /      ___\
       pi   I*log\2 + \/ 3 /
x6 = - -- - ----------------
       2           2
$$x_{6} = - \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}$$ 
               /      ___\
     pi   I*log\2 - \/ 3 /
x7 = -- - ----------------
     2           2
$$x_{7} = \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}$$ 
               /      ___\
     pi   I*log\2 + \/ 3 /
x8 = -- - ----------------
     2           2
$$x_{8} = \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}$$ 
x8 = pi/2 - i*log(sqrt(3) + 2)/2
Respuesta numérica [src] 
x1 = 520.718982332508
x2 = -296.095107600838
x3 = 55.7632696012188
x4 = -33.7721210260903
x5 = 3.92699081698724
x6 = -16.4933614313464
x7 = -47.9092879672443
x8 = 46.3384916404494
x9 = 16.4933614313464
x10 = -76.1836218495525
x11 = 90.3207887907066
x12 = 60.4756585816035
x13 = -99.7455667514759
x14 = -98.174770424681
x15 = -10.2101761241668
x16 = -85.6083998103219
x17 = -55.7632696012188
x18 = 32.2013246992954
x19 = 18.0641577581413
x20 = -82.4668071567321
x21 = -15612.9300901779
x22 = -91.8915851175014
x23 = -850.586210959436
x24 = 77.7544181763474
x25 = -90.3207887907066
x26 = -60.4756585816035
x27 = 91.8915851175014
x28 = -3.92699081698724
x29 = -463374.70622837
x30 = -71.4712328691678
x31 = 40.0553063332699
x32 = -25.9181393921158
x33 = 49.4800842940392
x34 = 33.7721210260903
x35 = 2.35619449019234
x36 = 47.9092879672443
x37 = 99.7455667514759
x38 = -11.7809724509617
x39 = -62.0464549083984
x40 = -18.0641577581413
x41 = 82.4668071567321
x42 = 54.1924732744239
x43 = 5.49778714378214
x44 = -49.4800842940392
x45 = 84.037603483527
x46 = 88.7499924639117
x47 = -77.7544181763474
x48 = 24.3473430653209
x49 = -2110.36486504894
x50 = -38.484510006475
x51 = 22.776546738526
x52 = 44.7676953136546
x53 = 62.0464549083984
x54 = 76.1836218495525
x55 = 69.9004365423729
x56 = -69.9004365423729
x57 = 68.329640215578
x58 = -63.6172512351933
x59 = 98.174770424681
x60 = -19.6349540849362
x61 = -101.316363078271
x62 = -93.4623814442964
x63 = -41.6261026600648
x64 = -27.4889357189107
x65 = -30.6305283725005
x66 = -84.037603483527
x67 = 10.2101761241668
x68 = 25.9181393921158
x69 = 74.6128255227576
x70 = -68.329640215578
x71 = -40.0553063332699
x72 = 11.7809724509617
x73 = -54.1924732744239
x74 = 896.139304436488
x75 = -32.2013246992954
x76 = 27.4889357189107
x77 = 38.484510006475
x78 = -5.49778714378214
x79 = 66.7588438887831
x79 = 66.7588438887831
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