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(sin(x)-(sqrt(3)/2))*sqrt(3*x^2-7*x+4)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
/           ___\    ________________    
|         \/ 3 |   /    2               
|sin(x) - -----|*\/  3*x  - 7*x + 4  = 0
\           2  /                        
$$\sqrt{\left(3 x^{2} - 7 x\right) + 4} \left(\sin{\left(x \right)} - \frac{\sqrt{3}}{2}\right) = 0$$
Gráfica
Suma y producto de raíces [src]
suma
          pi   2*pi
1 + 4/3 + -- + ----
          3     3  
$$\frac{2 \pi}{3} + \left(\frac{\pi}{3} + \left(1 + \frac{4}{3}\right)\right)$$
=
7/3 + pi
$$\frac{7}{3} + \pi$$
producto
  pi     
4*--     
  3  2*pi
----*----
 3    3  
$$\frac{2 \pi}{3} \frac{4 \frac{\pi}{3}}{3}$$
=
    2
8*pi 
-----
  27 
$$\frac{8 \pi^{2}}{27}$$
8*pi^2/27
Respuesta rápida [src]
x1 = 1
$$x_{1} = 1$$
x2 = 4/3
$$x_{2} = \frac{4}{3}$$
     pi
x3 = --
     3 
$$x_{3} = \frac{\pi}{3}$$
     2*pi
x4 = ----
      3  
$$x_{4} = \frac{2 \pi}{3}$$
x4 = 2*pi/3
Respuesta numérica [src]
x1 = -55.5014702134197
x2 = 90.0589894029074
x3 = -11.5191730631626
x4 = 52.3598775598299
x5 = -4075.69286925716
x6 = 39.7935069454707
x7 = -42.9350995990605
x8 = -30.3687289847013
x9 = 33.5103216382911
x10 = -48.1710873550435
x11 = 642.979296434711
x12 = -1197.99399856891
x13 = -49.2182849062401
x14 = -35.6047167406843
x15 = 8.37758040957278
x16 = 38.7463093942741
x17 = -16.7551608191456
x18 = -74.3510261349584
x19 = -73.3038285837618
x20 = -92.1533845053006
x21 = 51.3126800086333
x22 = -67.0206432765823
x23 = 95.2949771588904
x24 = 27.2271363311115
x25 = -85.870199198121
x26 = -29.3215314335047
x27 = -99.4837673636768
x28 = -54.4542726622231
x29 = 76.4454212373516
x30 = 64.9262481741891
x31 = 58.6430628670095
x32 = 82.7286065445312
x33 = 26.1799387799149
x34 = 77.4926187885482
x35 = 57.5958653158129
x36 = -61.7846555205993
x37 = 83.7758040957278
x38 = -17.8023583703422
x39 = -98.4365698124802
x40 = -60.7374579694027
x41 = 45.0294947014537
x42 = 32.4631240870945
x43 = 71.2094334813686
x44 = 70.162235930172
x45 = -80.634211442138
x46 = 101.57816246607
x47 = 20.943951023932
x48 = -5.23598775598299
x49 = 89.0117918517108
x50 = -68.0678408277789
x51 = -10.471975511966
x52 = -24.0855436775217
x53 = -79.5870138909414
x54 = -23.0383461263252
x55 = -93.2005820564972
x56 = -41.8879020478639
x57 = 63.8790506229925
x58 = -4.18879020478639
x59 = 1.0471975511966
x60 = 2.0943951023932
x61 = -36.6519142918809
x62 = 7.33038285837618
x63 = 19.8967534727354
x64 = -287.979326579064
x65 = -86.9173967493176
x66 = 46.0766922526503
x67 = 13.6135681655558
x68 = 14.6607657167524
x69 = 96.342174710087
x69 = 96.342174710087