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2sin²x+9sinxcosx+10cosx²=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     2                              2       
2*sin (x) + 9*sin(x)*cos(x) + 10*cos (x) = 0
(2sin⁡2(x)+9sin⁡(x)cos⁡(x))+10cos⁡2(x)=0\left(2 \sin^{2}{\left(x \right)} + 9 \sin{\left(x \right)} \cos{\left(x \right)}\right) + 10 \cos^{2}{\left(x \right)} = 0
Simplificar
Gráfica
0-80-60-40-2020406080-10010020-10
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
      /      ____\         /      ____\         /      ___\         /      ___\
      |2   \/ 29 |         |2   \/ 29 |         |1   \/ 5 |         |1   \/ 5 |
2*atan|- - ------| + 2*atan|- + ------| + 2*atan|- - -----| + 2*atan|- + -----|
      \5     5   /         \5     5   /         \2     2  /         \2     2  /
(2atan⁡(12−52)+(2atan⁡(25−295)+2atan⁡(25+295)))+2atan⁡(12+52)\left(2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} + \left(2 \operatorname{atan}{\left(\frac{2}{5} - \frac{\sqrt{29}}{5} \right)} + 2 \operatorname{atan}{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)}\right)\right) + 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} 
=
      /      ___\         /      ___\         /      ____\         /      ____\
      |1   \/ 5 |         |1   \/ 5 |         |2   \/ 29 |         |2   \/ 29 |
2*atan|- + -----| + 2*atan|- - -----| + 2*atan|- - ------| + 2*atan|- + ------|
      \2     2  /         \2     2  /         \5     5   /         \5     5   /
2atan⁡(25−295)+2atan⁡(12−52)+2atan⁡(25+295)+2atan⁡(12+52)2 \operatorname{atan}{\left(\frac{2}{5} - \frac{\sqrt{29}}{5} \right)} + 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} + 2 \operatorname{atan}{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)} + 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} 
producto
      /      ____\       /      ____\       /      ___\       /      ___\
      |2   \/ 29 |       |2   \/ 29 |       |1   \/ 5 |       |1   \/ 5 |
2*atan|- - ------|*2*atan|- + ------|*2*atan|- - -----|*2*atan|- + -----|
      \5     5   /       \5     5   /       \2     2  /       \2     2  /
2atan⁡(25−295)2atan⁡(25+295)2atan⁡(12−52)2atan⁡(12+52)2 \operatorname{atan}{\left(\frac{2}{5} - \frac{\sqrt{29}}{5} \right)} 2 \operatorname{atan}{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)} 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} 
=
       /      ___\     /      ___\     /      ____\     /      ____\
       |1   \/ 5 |     |1   \/ 5 |     |2   \/ 29 |     |2   \/ 29 |
16*atan|- + -----|*atan|- - -----|*atan|- - ------|*atan|- + ------|
       \2     2  /     \2     2  /     \5     5   /     \5     5   /
16atan⁡(25−295)atan⁡(25+295)atan⁡(12−52)atan⁡(12+52)16 \operatorname{atan}{\left(\frac{2}{5} - \frac{\sqrt{29}}{5} \right)} \operatorname{atan}{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)} \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} 
16*atan(1/2 + sqrt(5)/2)*atan(1/2 - sqrt(5)/2)*atan(2/5 - sqrt(29)/5)*atan(2/5 + sqrt(29)/5)
Respuesta rápida [src] 
           /      ____\
           |2   \/ 29 |
x1 = 2*atan|- - ------|
           \5     5   /
x1=2atan⁡(25−295)x_{1} = 2 \operatorname{atan}{\left(\frac{2}{5} - \frac{\sqrt{29}}{5} \right)} 
           /      ____\
           |2   \/ 29 |
x2 = 2*atan|- + ------|
           \5     5   /
x2=2atan⁡(25+295)x_{2} = 2 \operatorname{atan}{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)} 
           /      ___\
           |1   \/ 5 |
x3 = 2*atan|- - -----|
           \2     2  /
x3=2atan⁡(12−52)x_{3} = 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} 
           /      ___\
           |1   \/ 5 |
x4 = 2*atan|- + -----|
           \2     2  /
x4=2atan⁡(12+52)x_{4} = 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} 
x4 = 2*atan(1/2 + sqrt(5)/2)
Respuesta numérica [src] 
x1 = -73.4469209822478
x2 = 2.0344439357957
x3 = 61.7247043540018
x4 = -51.4557724071192
x5 = 99.4238161970793
x6 = -26.2398899465124
x7 = -57.7389577142988
x8 = -4.24874137138388
x9 = -92.2133356718981
x10 = 96.2822235434895
x11 = -16.8982532176315
x12 = 36.508821893395
x13 = 74.2079337364725
x14 = 8.23448801108685
x15 = 24.0255925109243
x16 = 42.7920072005746
x17 = -98.4965209790777
x18 = -67.1637356750682
x19 = 93.0574896580113
x20 = 5.1760365893855
x21 = 11.4592218965651
x22 = 77.4326676219507
x23 = -38.88940179276
x24 = -60.7974091360002
x25 = -1.19028994968253
x26 = 71.0663410828827
x27 = -45.1725870999396
x28 = -29.4646238319907
x29 = 27.0840439326256
x30 = 17.7424072037447
x31 = 80.4911190436521
x32 = 52.216785161344
x33 = 89.9990382363099
x34 = -104.779706286257
x35 = 168.455713344166
x36 = -7.47347525686212
x37 = 20.800858625446
x38 = -151.903596090104
x39 = 93.1406308898997
x40 = 39.7335557788732
x41 = 99.3406749651909
x42 = 49.0751925077542
x43 = 58.4999704685235
x44 = 30.2256365862154
x45 = -54.5142238288206
x46 = 14.5176733182664
x47 = 86.7743043508317
x48 = -42415.7495648336
x49 = -38.8062605608716
x50 = -86.0132915966069
x51 = -64.0221430214784
x52 = -13.7566605640417
x53 = -89.1548842501967
x54 = -286.992080194465
x55 = -82.8716989430172
x56 = 27.167185164514
x57 = 33.4503704716936
x58 = -34630.8829692381
x59 = -41.9478532144614
x60 = -35.7478091391703
x61 = 68.0078896611814
x62 = 46.0167410860528
x63 = -60.8805503678886
x64 = -32.523075253692
x65 = 71.1494823147711
x66 = -70.2221870967695
x67 = 49.1583337396426
x68 = -23.1814385248111
x69 = 83.7158529291303
x70 = -79.7301062894274
x71 = -95.4380695573763
x72 = -48.231038521641
x73 = -10.5319266785635
x74 = 64.7831557757031
x75 = -76.5053724039491
x76 = -16.8151119857431
x77 = -82.7885577111287
x78 = 55.4415190468222
x79 = -19.9567046393328
x80 = 5.09289535749705
x80 = 5.09289535749705
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