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√(3+4cos2x)=√2cosx la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
  ________________     __________
\/ 3 + 4*cos(2*x)  = \/ 2*cos(x) 
$$\sqrt{4 \cos{\left(2 x \right)} + 3} = \sqrt{2 \cos{\left(x \right)}}$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      3  
$$x_{1} = - \frac{\pi}{3}$$
     pi
x2 = --
     3 
$$x_{2} = \frac{\pi}{3}$$
           /          ____\
           |  1   I*\/ 15 |
x3 = -I*log|- - - --------|
           \  4      4    /
$$x_{3} = - i \log{\left(- \frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}$$
x3 = -i*log(-1/4 - sqrt(15)*i/4)
Suma y producto de raíces [src]
suma
                 /          ____\
  pi   pi        |  1   I*\/ 15 |
- -- + -- - I*log|- - - --------|
  3    3         \  4      4    /
$$- i \log{\left(- \frac{1}{4} - \frac{\sqrt{15} i}{4} \right)} + \left(- \frac{\pi}{3} + \frac{\pi}{3}\right)$$
=
      /          ____\
      |  1   I*\/ 15 |
-I*log|- - - --------|
      \  4      4    /
$$- i \log{\left(- \frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}$$
producto
        /      /          ____\\
-pi  pi |      |  1   I*\/ 15 ||
----*--*|-I*log|- - - --------||
 3   3  \      \  4      4    //
$$- i \log{\left(- \frac{1}{4} - \frac{\sqrt{15} i}{4} \right)} - \frac{\pi}{3} \frac{\pi}{3}$$
=
         /          ____\
    2    |  1   I*\/ 15 |
I*pi *log|- - - --------|
         \  4      4    /
-------------------------
            9            
$$\frac{i \pi^{2} \log{\left(- \frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}}{9}$$
i*pi^2*log(-1/4 - i*sqrt(15)/4)/9
Respuesta numérica [src]
x1 = -13.6135681655558
x2 = -93.2005820564972
x3 = -55.5014702134197
x4 = -76.4454212373516
x5 = -36.6519142918809
x6 = 55.5014702134197
x7 = 32.4631240870945
x8 = -24.0855436775217
x9 = -26.1799387799149
x10 = 13.6135681655558
x11 = 99.4837673636768
x12 = -68.0678408277789
x13 = 82.7286065445312
x14 = 63.8790506229925
x15 = -19.8967534727354
x16 = -1.0471975511966
x17 = 30.3687289847013
x18 = 68.0678408277789
x19 = -49.2182849062401
x20 = 38.7463093942741
x21 = 86.9173967493176
x22 = 11.5191730631626
x23 = -99.4837673636768
x24 = 61.7846555205993
x25 = 36.6519142918809
x26 = 24.0855436775217
x27 = -42.9350995990605
x28 = -57.5958653158129
x29 = -5.23598775598299
x30 = 80.634211442138
x31 = -32.4631240870945
x32 = -89.0117918517108
x33 = 17.8023583703422
x34 = -11.5191730631626
x35 = -79.8579324113977
x36 = 26.1799387799149
x37 = 7.33038285837618
x38 = -63.8790506229925
x39 = 19.8967534727354
x40 = -95.2949771588904
x41 = -70.162235930172
x42 = -17.8023583703422
x43 = 74.3510261349584
x44 = 70.162235930172
x45 = -51.3126800086333
x46 = -61.7846555205993
x47 = 76.4454212373516
x48 = -7.33038285837618
x49 = -38.7463093942741
x49 = -38.7463093942741