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tan(2*p/3+3*x)+tan(7*p/9-x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /2*p      \      /7*p    \    
tan|--- + 3*x| + tan|--- - x| = 0
   \ 3       /      \ 9     /
tan⁡(2p3+3x)+tan⁡(7p9−x)=0\tan{\left(\frac{2 p}{3} + 3 x \right)} + \tan{\left(\frac{7 p}{9} - x \right)} = 0
Simplificar
Gráfica
Respuesta rápida [src] 
            /|     __________|\      /        __________\
            ||    /  -26*I*p ||      |       /  -26*I*p |
            ||   /   ------- ||      |      /   ------- |
            ||4 /       9    ||      |   4 /       9    |
x1 = - I*log\|\/    e        |/ + arg\-I*\/    e        /
x1=−ilog⁡(∣e−26ip94∣)+arg⁡(−ie−26ip94)x_{1} = - i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} + \arg{\left(- i \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)} 
            /|     __________|\      /       __________\
            ||    /  -26*I*p ||      |      /  -26*I*p |
            ||   /   ------- ||      |     /   ------- |
            ||4 /       9    ||      |  4 /       9    |
x2 = - I*log\|\/    e        |/ + arg\I*\/    e        /
x2=−ilog⁡(∣e−26ip94∣)+arg⁡(ie−26ip94)x_{2} = - i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} + \arg{\left(i \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)} 
            /|     __________|\      /      __________\
            ||    /  -26*I*p ||      |     /  -26*I*p |
            ||   /   ------- ||      |    /   ------- |
            ||4 /       9    ||      | 4 /       9    |
x3 = - I*log\|\/    e        |/ + arg\-\/    e        /
x3=−ilog⁡(∣e−26ip94∣)+arg⁡(−e−26ip94)x_{3} = - i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} + \arg{\left(- \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)} 
        / -26*I*p\             
        | -------|             
        |    9   |             
     arg\e       /   13*I*im(p)
x4 = ------------- - ----------
           4             18
x4=−13iim⁡(p)18+arg⁡(e−26ip9)4x_{4} = - \frac{13 i \operatorname{im}{\left(p\right)}}{18} + \frac{\arg{\left(e^{- \frac{26 i p}{9}} \right)}}{4} 
x4 = -13*i*im(p)/18 + arg(exp(-26*i*p/9))/4
Suma y producto de raíces [src] 
suma
       /|     __________|\      /        __________\          /|     __________|\      /       __________\          /|     __________|\      /      __________\      / -26*I*p\             
       ||    /  -26*I*p ||      |       /  -26*I*p |          ||    /  -26*I*p ||      |      /  -26*I*p |          ||    /  -26*I*p ||      |     /  -26*I*p |      | -------|             
       ||   /   ------- ||      |      /   ------- |          ||   /   ------- ||      |     /   ------- |          ||   /   ------- ||      |    /   ------- |      |    9   |             
       ||4 /       9    ||      |   4 /       9    |          ||4 /       9    ||      |  4 /       9    |          ||4 /       9    ||      | 4 /       9    |   arg\e       /   13*I*im(p)
- I*log\|\/    e        |/ + arg\-I*\/    e        / + - I*log\|\/    e        |/ + arg\I*\/    e        / + - I*log\|\/    e        |/ + arg\-\/    e        / + ------------- - ----------
                                                                                                                                                                        4             18
(−13iim⁡(p)18+arg⁡(e−26ip9)4)+((−ilog⁡(∣e−26ip94∣)+arg⁡(−e−26ip94))+((−ilog⁡(∣e−26ip94∣)+arg⁡(−ie−26ip94))+(−ilog⁡(∣e−26ip94∣)+arg⁡(ie−26ip94))))\left(- \frac{13 i \operatorname{im}{\left(p\right)}}{18} + \frac{\arg{\left(e^{- \frac{26 i p}{9}} \right)}}{4}\right) + \left(\left(- i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} + \arg{\left(- \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)}\right) + \left(\left(- i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} + \arg{\left(- i \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)}\right) + \left(- i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} + \arg{\left(i \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)}\right)\right)\right) 
=
   / -26*I*p\          /|     __________|\                   /      __________\      /       __________\      /        __________\
   | -------|          ||    /  -26*I*p ||                   |     /  -26*I*p |      |      /  -26*I*p |      |       /  -26*I*p |
   |    9   |          ||   /   ------- ||                   |    /   ------- |      |     /   ------- |      |      /   ------- |
arg\e       /          ||4 /       9    ||   13*I*im(p)      | 4 /       9    |      |  4 /       9    |      |   4 /       9    |
------------- - 3*I*log\|\/    e        |/ - ---------- + arg\-\/    e        / + arg\I*\/    e        / + arg\-I*\/    e        /
      4                                          18
−3ilog⁡(∣e−26ip94∣)−13iim⁡(p)18+arg⁡(−ie−26ip94)+arg⁡(ie−26ip94)+arg⁡(−e−26ip94)+arg⁡(e−26ip9)4- 3 i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} - \frac{13 i \operatorname{im}{\left(p\right)}}{18} + \arg{\left(- i \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)} + \arg{\left(i \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)} + \arg{\left(- \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)} + \frac{\arg{\left(e^{- \frac{26 i p}{9}} \right)}}{4} 
producto
/       /|     __________|\      /        __________\\ /       /|     __________|\      /       __________\\ /       /|     __________|\      /      __________\\ /   / -26*I*p\             \
|       ||    /  -26*I*p ||      |       /  -26*I*p || |       ||    /  -26*I*p ||      |      /  -26*I*p || |       ||    /  -26*I*p ||      |     /  -26*I*p || |   | -------|             |
|       ||   /   ------- ||      |      /   ------- || |       ||   /   ------- ||      |     /   ------- || |       ||   /   ------- ||      |    /   ------- || |   |    9   |             |
|       ||4 /       9    ||      |   4 /       9    || |       ||4 /       9    ||      |  4 /       9    || |       ||4 /       9    ||      | 4 /       9    || |arg\e       /   13*I*im(p)|
\- I*log\|\/    e        |/ + arg\-I*\/    e        //*\- I*log\|\/    e        |/ + arg\I*\/    e        //*\- I*log\|\/    e        |/ + arg\-\/    e        //*|------------- - ----------|
                                                                                                                                                                  \      4             18    /
(−ilog⁡(∣e−26ip94∣)+arg⁡(−ie−26ip94))(−ilog⁡(∣e−26ip94∣)+arg⁡(ie−26ip94))(−ilog⁡(∣e−26ip94∣)+arg⁡(−e−26ip94))(−13iim⁡(p)18+arg⁡(e−26ip9)4)\left(- i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} + \arg{\left(- i \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)}\right) \left(- i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} + \arg{\left(i \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)}\right) \left(- i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} + \arg{\left(- \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)}\right) \left(- \frac{13 i \operatorname{im}{\left(p\right)}}{18} + \frac{\arg{\left(e^{- \frac{26 i p}{9}} \right)}}{4}\right) 
=
/     /      __________\        /|     __________|\\ /     /       __________\        /|     __________|\\ /     /        __________\        /|     __________|\\                                 
|     |     /  -26*I*p |        ||    /  -26*I*p ||| |     |      /  -26*I*p |        ||    /  -26*I*p ||| |     |       /  -26*I*p |        ||    /  -26*I*p ||| /       / -26*I*p\             \
|     |    /   ------- |        ||   /   ------- ||| |     |     /   ------- |        ||   /   ------- ||| |     |      /   ------- |        ||   /   ------- ||| |       | -------|             |
|     | 4 /       9    |        ||4 /       9    ||| |     |  4 /       9    |        ||4 /       9    ||| |     |   4 /       9    |        ||4 /       9    ||| |       |    9   |             |
\- arg\-\/    e        / + I*log\|\/    e        |//*\- arg\I*\/    e        / + I*log\|\/    e        |//*\- arg\-I*\/    e        / + I*log\|\/    e        |//*\- 9*arg\e       / + 26*I*im(p)/
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                36
(ilog⁡(∣e−26ip94∣)−arg⁡(−ie−26ip94))(ilog⁡(∣e−26ip94∣)−arg⁡(ie−26ip94))(ilog⁡(∣e−26ip94∣)−arg⁡(−e−26ip94))(26iim⁡(p)−9arg⁡(e−26ip9))36\frac{\left(i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} - \arg{\left(- i \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)}\right) \left(i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} - \arg{\left(i \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)}\right) \left(i \log{\left(\left|{\sqrt[4]{e^{- \frac{26 i p}{9}}}}\right| \right)} - \arg{\left(- \sqrt[4]{e^{- \frac{26 i p}{9}}} \right)}\right) \left(26 i \operatorname{im}{\left(p\right)} - 9 \arg{\left(e^{- \frac{26 i p}{9}} \right)}\right)}{36} 
(-arg(-exp(-26*i*p/9)^(1/4)) + i*log(Abs(exp(-26*i*p/9)^(1/4))))*(-arg(i*exp(-26*i*p/9)^(1/4)) + i*log(Abs(exp(-26*i*p/9)^(1/4))))*(-arg(-i*exp(-26*i*p/9)^(1/4)) + i*log(Abs(exp(-26*i*p/9)^(1/4))))*(-9*arg(exp(-26*i*p/9)) + 26*i*im(p))/36
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