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sin(arctg3x)=3x/√1+9x^2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                  3*x       2
sin(atan(3*x)) = ----- + 9*x 
                   ___       
                 \/ 1        
$$\sin{\left(\operatorname{atan}{\left(3 x \right)} \right)} = 9 x^{2} + \frac{3 x}{\sqrt{1}}$$
Gráfica
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
                                        _____________     /           _____________                        \
                                       /        ____      |          /        ____                         |
                                      /  17   \/ 33       |  ___    /  17   \/ 33                          |
                                   3 /   -- + ------      |\/ 3 *3 /   -- + ------              ___        |
       2             1             \/    27     9         |      \/    27     9               \/ 3         |
x2 = - - - --------------------- + ------------------ + I*|------------------------ + ---------------------|
       9           _____________           6              |           6                       _____________|
                  /        ____                           |                                  /        ____ |
                 /  17   \/ 33                            |                                 /  17   \/ 33  |
           27*3 /   -- + ------                           |                           27*3 /   -- + ------ |
              \/    27     9                              \                              \/    27     9    /
$$x_{2} = - \frac{2}{9} - \frac{1}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6} + i \left(\frac{\sqrt{3}}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt{3} \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6}\right)$$
                                        _____________     /             _____________                        \
                                       /        ____      |            /        ____                         |
                                      /  17   \/ 33       |    ___    /  17   \/ 33                          |
                                   3 /   -- + ------      |  \/ 3 *3 /   -- + ------              ___        |
       2             1             \/    27     9         |        \/    27     9               \/ 3         |
x3 = - - - --------------------- + ------------------ + I*|- ------------------------ - ---------------------|
       9           _____________           6              |             6                       _____________|
                  /        ____                           |                                    /        ____ |
                 /  17   \/ 33                            |                                   /  17   \/ 33  |
           27*3 /   -- + ------                           |                             27*3 /   -- + ------ |
              \/    27     9                              \                                \/    27     9    /
$$x_{3} = - \frac{2}{9} - \frac{1}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6} - \frac{\sqrt{3}}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}\right)$$
x3 = -2/9 - 1/(27*(17/27 + sqrt(33)/9)^(1/3)) + (17/27 + sqrt(33)/9)^(1/3)/6 + i*(-sqrt(3)*(17/27 + sqrt(33)/9)^(1/3)/6 - sqrt(3)/(27*(17/27 + sqrt(33)/9)^(1/3)))
Suma y producto de raíces [src]
suma
                                   _____________     /           _____________                        \                                      _____________     /             _____________                        \
                                  /        ____      |          /        ____                         |                                     /        ____      |            /        ____                         |
                                 /  17   \/ 33       |  ___    /  17   \/ 33                          |                                    /  17   \/ 33       |    ___    /  17   \/ 33                          |
                              3 /   -- + ------      |\/ 3 *3 /   -- + ------              ___        |                                 3 /   -- + ------      |  \/ 3 *3 /   -- + ------              ___        |
  2             1             \/    27     9         |      \/    27     9               \/ 3         |     2             1             \/    27     9         |        \/    27     9               \/ 3         |
- - - --------------------- + ------------------ + I*|------------------------ + ---------------------| + - - - --------------------- + ------------------ + I*|- ------------------------ - ---------------------|
  9           _____________           6              |           6                       _____________|     9           _____________           6              |             6                       _____________|
             /        ____                           |                                  /        ____ |                /        ____                           |                                    /        ____ |
            /  17   \/ 33                            |                                 /  17   \/ 33  |               /  17   \/ 33                            |                                   /  17   \/ 33  |
      27*3 /   -- + ------                           |                           27*3 /   -- + ------ |         27*3 /   -- + ------                           |                             27*3 /   -- + ------ |
         \/    27     9                              \                              \/    27     9    /            \/    27     9                              \                                \/    27     9    /
$$\left(- \frac{2}{9} - \frac{1}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6} - \frac{\sqrt{3}}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}\right)\right) + \left(- \frac{2}{9} - \frac{1}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6} + i \left(\frac{\sqrt{3}}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt{3} \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6}\right)\right)$$
=
                                   _____________     /             _____________                        \     /           _____________                        \
                                  /        ____      |            /        ____                         |     |          /        ____                         |
                                 /  17   \/ 33       |    ___    /  17   \/ 33                          |     |  ___    /  17   \/ 33                          |
                              3 /   -- + ------      |  \/ 3 *3 /   -- + ------              ___        |     |\/ 3 *3 /   -- + ------              ___        |
  4             2             \/    27     9         |        \/    27     9               \/ 3         |     |      \/    27     9               \/ 3         |
- - - --------------------- + ------------------ + I*|- ------------------------ - ---------------------| + I*|------------------------ + ---------------------|
  9           _____________           3              |             6                       _____________|     |           6                       _____________|
             /        ____                           |                                    /        ____ |     |                                  /        ____ |
            /  17   \/ 33                            |                                   /  17   \/ 33  |     |                                 /  17   \/ 33  |
      27*3 /   -- + ------                           |                             27*3 /   -- + ------ |     |                           27*3 /   -- + ------ |
         \/    27     9                              \                                \/    27     9    /     \                              \/    27     9    /
$$- \frac{4}{9} - \frac{2}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6} - \frac{\sqrt{3}}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}\right) + i \left(\frac{\sqrt{3}}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt{3} \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6}\right)$$
producto
  /                                   _____________     /           _____________                        \\ /                                   _____________     /             _____________                        \\
  |                                  /        ____      |          /        ____                         || |                                  /        ____      |            /        ____                         ||
  |                                 /  17   \/ 33       |  ___    /  17   \/ 33                          || |                                 /  17   \/ 33       |    ___    /  17   \/ 33                          ||
  |                              3 /   -- + ------      |\/ 3 *3 /   -- + ------              ___        || |                              3 /   -- + ------      |  \/ 3 *3 /   -- + ------              ___        ||
  |  2             1             \/    27     9         |      \/    27     9               \/ 3         || |  2             1             \/    27     9         |        \/    27     9               \/ 3         ||
0*|- - - --------------------- + ------------------ + I*|------------------------ + ---------------------||*|- - - --------------------- + ------------------ + I*|- ------------------------ - ---------------------||
  |  9           _____________           6              |           6                       _____________|| |  9           _____________           6              |             6                       _____________||
  |             /        ____                           |                                  /        ____ || |             /        ____                           |                                    /        ____ ||
  |            /  17   \/ 33                            |                                 /  17   \/ 33  || |            /  17   \/ 33                            |                                   /  17   \/ 33  ||
  |      27*3 /   -- + ------                           |                           27*3 /   -- + ------ || |      27*3 /   -- + ------                           |                             27*3 /   -- + ------ ||
  \         \/    27     9                              \                              \/    27     9    // \         \/    27     9                              \                                \/    27     9    //
$$0 \left(- \frac{2}{9} - \frac{1}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6} + i \left(\frac{\sqrt{3}}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt{3} \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6}\right)\right) \left(- \frac{2}{9} - \frac{1}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{\sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}{6} - \frac{\sqrt{3}}{27 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}\right)\right)$$
=
0
$$0$$
0
Respuesta numérica [src]
x1 = 0
x2 = -0.0760518312179873 + 0.371714169346646*i
x3 = -0.0760518312179873 - 0.371714169346646*i
x3 = -0.0760518312179873 - 0.371714169346646*i