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((-2*sin(x)-sqrt(3)*sin^(2)(x)-sqrt(3)*cos^(2)(x)))/((2+sqrt(3)*sin(x))^(2))=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
              ___    2        ___    2       
-2*sin(x) - \/ 3 *sin (x) - \/ 3 *cos (x)    
----------------------------------------- = 0
                             2               
           /      ___       \                
           \2 + \/ 3 *sin(x)/                
$$\frac{\left(- \sqrt{3} \sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)}\right) - \sqrt{3} \cos^{2}{\left(x \right)}}{\left(\sqrt{3} \sin{\left(x \right)} + 2\right)^{2}} = 0$$
Gráfica
Respuesta rápida [src]
     -2*pi
x1 = -----
       3  
$$x_{1} = - \frac{2 \pi}{3}$$
     -pi 
x2 = ----
      3  
$$x_{2} = - \frac{\pi}{3}$$
x2 = -pi/3
Suma y producto de raíces [src]
suma
  2*pi   pi
- ---- - --
   3     3 
$$- \frac{2 \pi}{3} - \frac{\pi}{3}$$
=
-pi
$$- \pi$$
producto
-2*pi -pi 
-----*----
  3    3  
$$- \frac{2 \pi}{3} \left(- \frac{\pi}{3}\right)$$
=
    2
2*pi 
-----
  9  
$$\frac{2 \pi^{2}}{9}$$
2*pi^2/9
Respuesta numérica [src]
x1 = -39.7935069454707
x2 = -83.7758040957278
x3 = 4.18879020478639
x4 = -13.6135681655558
x5 = 55.5014702134197
x6 = -19.8967534727354
x7 = 98.4365698124802
x8 = -63.8790506229925
x9 = 24.0855436775217
x10 = 30.3687289847013
x11 = 5.23598775598299
x12 = 92.1533845053006
x13 = 74.3510261349584
x14 = 48.1710873550435
x15 = 17.8023583703422
x16 = -26.1799387799149
x17 = -2.0943951023932
x18 = -90.0589894029074
x19 = -57.5958653158129
x20 = 104.71975511966
x21 = 68.0678408277789
x22 = 41.8879020478639
x23 = 85.870199198121
x24 = -70.162235930172
x25 = -46.0766922526503
x25 = -46.0766922526503