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La ecuación:
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Ecuación 3*x=5
Expresar {x} en función de y en la ecuación:
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17*x-19*y=-12
-4*x+14*y=-2
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Expresiones con funciones
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Seno sin
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cos(x)^(2)+2*sin(2x)-3=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

   2                        
cos (x) + 2*sin(2*x) - 3 = 0

\left(2 \sin{\left(2 x \right)} + \cos^{2}{\left(x \right)}\right) - 3 = 0

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

         /         ___\                                          
         |20 - 8*\/ 2 |                                          
     atan|------------|     /             /   _________________\\
         |        ___ |     |             |  /             ___ ||
         \5 - 2*\/ 2  /     |log(17)   log\\/  561 - 340*\/ 2  /|
x1 = ------------------ + I*|------- - -------------------------|
             2              \   2                  2            /

x_{1} = \frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{561 - 340 \sqrt{2}} \right)}}{2} + \frac{\log{\left(17 \right)}}{2}\right)

         /         ___\                                          
         |20 + 8*\/ 2 |                                          
     atan|------------|     /             /   _________________\\
         |        ___ |     |             |  /             ___ ||
         \5 + 2*\/ 2  /     |log(17)   log\\/  561 + 340*\/ 2  /|
x2 = ------------------ + I*|------- - -------------------------|
             2              \   2                  2            /

x_{2} = \frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{340 \sqrt{2} + 561} \right)}}{2} + \frac{\log{\left(17 \right)}}{2}\right)

                                                         /   /    /         ___\\\
                                                         |   |    |20 - 8*\/ 2 |||
                                                         |   |atan|------------|||
                                                         |   |    |        ___ |||
                                                         |   |    \5 - 2*\/ 2  /||
             /             /   _________________\\       |sin|------------------||
             |log(17)      |4 /             ___ ||       |   \        2         /|
x3 = -pi + I*|------- - log\\/  561 - 340*\/ 2  /| + atan|-----------------------|
             \   2                               /       |   /    /         ___\\|
                                                         |   |    |20 - 8*\/ 2 |||
                                                         |   |atan|------------|||
                                                         |   |    |        ___ |||
                                                         |   |    \5 - 2*\/ 2  /||
                                                         |cos|------------------||
                                                         \   \        2         //

x_{3} = - \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{561 - 340 \sqrt{2}} \right)} + \frac{\log{\left(17 \right)}}{2}\right)

                                                         /   /    /         ___\\\
                                                         |   |    |20 + 8*\/ 2 |||
                                                         |   |atan|------------|||
                                                         |   |    |        ___ |||
                                                         |   |    \5 + 2*\/ 2  /||
             /             /   _________________\\       |sin|------------------||
             |log(17)      |4 /             ___ ||       |   \        2         /|
x4 = -pi + I*|------- - log\\/  561 + 340*\/ 2  /| + atan|-----------------------|
             \   2                               /       |   /    /         ___\\|
                                                         |   |    |20 + 8*\/ 2 |||
                                                         |   |atan|------------|||
                                                         |   |    |        ___ |||
                                                         |   |    \5 + 2*\/ 2  /||
                                                         |cos|------------------||
                                                         \   \        2         //

x_{4} = - \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{340 \sqrt{2} + 561} \right)} + \frac{\log{\left(17 \right)}}{2}\right)

x4 = -pi + atan(sin(atan((8*sqrt(2) + 20)/(2*sqrt(2) + 5))/2)/cos(atan((8*sqrt(2) + 20)/(2*sqrt(2) + 5))/2)) + i*(-log((340*sqrt(2) + 561)^(1/4)) + log(17)/2)

Suma y producto de raíces [src]

suma

                                                                                                                                                                                  /   /    /         ___\\\                                                       /   /    /         ___\\\
                                                                                                                                                                                  |   |    |20 - 8*\/ 2 |||                                                       |   |    |20 + 8*\/ 2 |||
    /         ___\                                                 /         ___\                                                                                                 |   |atan|------------|||                                                       |   |atan|------------|||
    |20 - 8*\/ 2 |                                                 |20 + 8*\/ 2 |                                                                                                 |   |    |        ___ |||                                                       |   |    |        ___ |||
atan|------------|     /             /   _________________\\   atan|------------|     /             /   _________________\\                                                       |   |    \5 - 2*\/ 2  /||                                                       |   |    \5 + 2*\/ 2  /||
    |        ___ |     |             |  /             ___ ||       |        ___ |     |             |  /             ___ ||           /             /   _________________\\       |sin|------------------||           /             /   _________________\\       |sin|------------------||
    \5 - 2*\/ 2  /     |log(17)   log\\/  561 - 340*\/ 2  /|       \5 + 2*\/ 2  /     |log(17)   log\\/  561 + 340*\/ 2  /|           |log(17)      |4 /             ___ ||       |   \        2         /|           |log(17)      |4 /             ___ ||       |   \        2         /|
------------------ + I*|------- - -------------------------| + ------------------ + I*|------- - -------------------------| + -pi + I*|------- - log\\/  561 - 340*\/ 2  /| + atan|-----------------------| + -pi + I*|------- - log\\/  561 + 340*\/ 2  /| + atan|-----------------------|
        2              \   2                  2            /           2              \   2                  2            /           \   2                               /       |   /    /         ___\\|           \   2                               /       |   /    /         ___\\|
                                                                                                                                                                                  |   |    |20 - 8*\/ 2 |||                                                       |   |    |20 + 8*\/ 2 |||
                                                                                                                                                                                  |   |atan|------------|||                                                       |   |atan|------------|||
                                                                                                                                                                                  |   |    |        ___ |||                                                       |   |    |        ___ |||
                                                                                                                                                                                  |   |    \5 - 2*\/ 2  /||                                                       |   |    \5 + 2*\/ 2  /||
                                                                                                                                                                                  |cos|------------------||                                                       |cos|------------------||
                                                                                                                                                                                  \   \        2         //                                                       \   \        2         //

\left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{340 \sqrt{2} + 561} \right)} + \frac{\log{\left(17 \right)}}{2}\right)\right) + \left(\left(\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{340 \sqrt{2} + 561} \right)}}{2} + \frac{\log{\left(17 \right)}}{2}\right)\right) + \left(\frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{561 - 340 \sqrt{2}} \right)}}{2} + \frac{\log{\left(17 \right)}}{2}\right)\right)\right) + \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{561 - 340 \sqrt{2}} \right)} + \frac{\log{\left(17 \right)}}{2}\right)\right)\right)

                                                                                                                                                                                                                             /   /    /         ___\\\       /   /    /         ___\\\
                                                                                                                                                                                                                             |   |    |20 - 8*\/ 2 |||       |   |    |20 + 8*\/ 2 |||
    /         ___\       /         ___\                                                                                                                                                                                      |   |atan|------------|||       |   |atan|------------|||
    |20 - 8*\/ 2 |       |20 + 8*\/ 2 |                                                                                                                                                                                      |   |    |        ___ |||       |   |    |        ___ |||
atan|------------|   atan|------------|                                                                                                /             /   _________________\\     /             /   _________________\\       |   |    \5 - 2*\/ 2  /||       |   |    \5 + 2*\/ 2  /||
    |        ___ |       |        ___ |            /             /   _________________\\     /             /   _________________\\     |             |  /             ___ ||     |             |  /             ___ ||       |sin|------------------||       |sin|------------------||
    \5 - 2*\/ 2  /       \5 + 2*\/ 2  /            |log(17)      |4 /             ___ ||     |log(17)      |4 /             ___ ||     |log(17)   log\\/  561 - 340*\/ 2  /|     |log(17)   log\\/  561 + 340*\/ 2  /|       |   \        2         /|       |   \        2         /|
------------------ + ------------------ - 2*pi + I*|------- - log\\/  561 - 340*\/ 2  /| + I*|------- - log\\/  561 + 340*\/ 2  /| + I*|------- - -------------------------| + I*|------- - -------------------------| + atan|-----------------------| + atan|-----------------------|
        2                    2                     \   2                               /     \   2                               /     \   2                  2            /     \   2                  2            /       |   /    /         ___\\|       |   /    /         ___\\|
                                                                                                                                                                                                                             |   |    |20 - 8*\/ 2 |||       |   |    |20 + 8*\/ 2 |||
                                                                                                                                                                                                                             |   |atan|------------|||       |   |atan|------------|||
                                                                                                                                                                                                                             |   |    |        ___ |||       |   |    |        ___ |||
                                                                                                                                                                                                                             |   |    \5 - 2*\/ 2  /||       |   |    \5 + 2*\/ 2  /||
                                                                                                                                                                                                                             |cos|------------------||       |cos|------------------||
                                                                                                                                                                                                                             \   \        2         //       \   \        2         //

- 2 \pi + \frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} + \frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{340 \sqrt{2} + 561} \right)} + \frac{\log{\left(17 \right)}}{2}\right) + i \left(- \frac{\log{\left(\sqrt{340 \sqrt{2} + 561} \right)}}{2} + \frac{\log{\left(17 \right)}}{2}\right) + i \left(- \log{\left(\sqrt[4]{561 - 340 \sqrt{2}} \right)} + \frac{\log{\left(17 \right)}}{2}\right) + i \left(- \frac{\log{\left(\sqrt{561 - 340 \sqrt{2}} \right)}}{2} + \frac{\log{\left(17 \right)}}{2}\right)

producto

                                                                                                                              /                                                    /   /    /         ___\\\\ /                                                    /   /    /         ___\\\\
                                                                                                                              |                                                    |   |    |20 - 8*\/ 2 |||| |                                                    |   |    |20 + 8*\/ 2 ||||
/    /         ___\                                          \ /    /         ___\                                          \ |                                                    |   |atan|------------|||| |                                                    |   |atan|------------||||
|    |20 - 8*\/ 2 |                                          | |    |20 + 8*\/ 2 |                                          | |                                                    |   |    |        ___ |||| |                                                    |   |    |        ___ ||||
|atan|------------|     /             /   _________________\\| |atan|------------|     /             /   _________________\\| |                                                    |   |    \5 - 2*\/ 2  /||| |                                                    |   |    \5 + 2*\/ 2  /|||
|    |        ___ |     |             |  /             ___ ||| |    |        ___ |     |             |  /             ___ ||| |        /             /   _________________\\       |sin|------------------||| |        /             /   _________________\\       |sin|------------------|||
|    \5 - 2*\/ 2  /     |log(17)   log\\/  561 - 340*\/ 2  /|| |    \5 + 2*\/ 2  /     |log(17)   log\\/  561 + 340*\/ 2  /|| |        |log(17)      |4 /             ___ ||       |   \        2         /|| |        |log(17)      |4 /             ___ ||       |   \        2         /||
|------------------ + I*|------- - -------------------------||*|------------------ + I*|------- - -------------------------||*|-pi + I*|------- - log\\/  561 - 340*\/ 2  /| + atan|-----------------------||*|-pi + I*|------- - log\\/  561 + 340*\/ 2  /| + atan|-----------------------||
\        2              \   2                  2            // \        2              \   2                  2            // |        \   2                               /       |   /    /         ___\\|| |        \   2                               /       |   /    /         ___\\||
                                                                                                                              |                                                    |   |    |20 - 8*\/ 2 |||| |                                                    |   |    |20 + 8*\/ 2 ||||
                                                                                                                              |                                                    |   |atan|------------|||| |                                                    |   |atan|------------||||
                                                                                                                              |                                                    |   |    |        ___ |||| |                                                    |   |    |        ___ ||||
                                                                                                                              |                                                    |   |    \5 - 2*\/ 2  /||| |                                                    |   |    \5 + 2*\/ 2  /|||
                                                                                                                              |                                                    |cos|------------------||| |                                                    |cos|------------------|||
                                                                                                                              \                                                    \   \        2         /// \                                                    \   \        2         ///

\left(\frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{561 - 340 \sqrt{2}} \right)}}{2} + \frac{\log{\left(17 \right)}}{2}\right)\right) \left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{340 \sqrt{2} + 561} \right)}}{2} + \frac{\log{\left(17 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{20 - 8 \sqrt{2}}{5 - 2 \sqrt{2}} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{561 - 340 \sqrt{2}} \right)} + \frac{\log{\left(17 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{2} + 20}{2 \sqrt{2} + 5} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{340 \sqrt{2} + 561} \right)} + \frac{\log{\left(17 \right)}}{2}\right)\right)

/  /     /          ___\          \          \ /  /     /          ___\          \          \ /          /     /          ___\          \          \ /          /     /          ___\          \          \
|I*\- log\33 - 20*\/ 2 / + log(17)/          | |I*\- log\33 + 20*\/ 2 / + log(17)/          | |        I*\- log\33 - 20*\/ 2 / + log(17)/          | |        I*\- log\33 + 20*\/ 2 / + log(17)/          |
|---------------------------------- + atan(4)|*|---------------------------------- + atan(4)|*|-2*pi + ---------------------------------- + atan(4)|*|-2*pi + ---------------------------------- + atan(4)|
\                2                           / \                2                           / \                        2                           / \                        2                           /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                     16

\frac{\left(\operatorname{atan}{\left(4 \right)} + \frac{i \left(- \log{\left(33 - 20 \sqrt{2} \right)} + \log{\left(17 \right)}\right)}{2}\right) \left(\operatorname{atan}{\left(4 \right)} + \frac{i \left(- \log{\left(20 \sqrt{2} + 33 \right)} + \log{\left(17 \right)}\right)}{2}\right) \left(- 2 \pi + \operatorname{atan}{\left(4 \right)} + \frac{i \left(- \log{\left(33 - 20 \sqrt{2} \right)} + \log{\left(17 \right)}\right)}{2}\right) \left(- 2 \pi + \operatorname{atan}{\left(4 \right)} + \frac{i \left(- \log{\left(20 \sqrt{2} + 33 \right)} + \log{\left(17 \right)}\right)}{2}\right)}{16}

(i*(-log(33 - 20*sqrt(2)) + log(17))/2 + atan(4))*(i*(-log(33 + 20*sqrt(2)) + log(17))/2 + atan(4))*(-2*pi + i*(-log(33 - 20*sqrt(2)) + log(17))/2 + atan(4))*(-2*pi + i*(-log(33 + 20*sqrt(2)) + log(17))/2 + atan(4))/16

Respuesta numérica [src]

x1 = -2.47868382175578 + 0.320577469865141*i

x2 = -2.47868382175578 - 0.320577469865141*i

x3 = 0.662908831834016 + 0.320577469865141*i

x4 = 0.662908831834016 - 0.320577469865141*i

x4 = 0.662908831834016 - 0.320577469865141*i

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Expresiones con funciones

cos(x)^(2)+2*sin(2x)-3=0 la ecuación

Solución numérica:

Solución