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La ecuación:
Ecuación -x/11+x=50/11
Ecuación 12/x=3
Ecuación 6-5(4x-1)=3
Ecuación 13/(x-5)=5/(x-13)
Expresar {x} en función de y en la ecuación:
-1*x+4*y=-10
-11*x-19*y=14
8*x+6*y=20
-11*x-1*y=15
Expresiones idénticas
8cos^ dos (x)(dos cos^2(x)- uno)= nueve
8 coseno de al cuadrado (x)(2 coseno de al cuadrado (x) menos 1) es igual a 9
8 coseno de en el grado dos (x)(dos coseno de al cuadrado (x) menos uno) es igual a nueve
8cos2(x)(2cos2(x)-1)=9
8cos2x2cos2x-1=9
8cos²(x)(2cos²(x)-1)=9
8cos en el grado 2(x)(2cos en el grado 2(x)-1)=9
8cos^2x2cos^2x-1=9
Expresiones semejantes
8cos^2(x)(2cos^2(x)+1)=9

8cos^2(x)(2cos^2(x)-1)=9 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

     2    /     2       \    
8*cos (x)*\2*cos (x) - 1/ = 9

\left(2 \cos^{2}{\left(x \right)} - 1\right) 8 \cos^{2}{\left(x \right)} = 9

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

                 /     ______________\
                 |    /         ____ |
     pi          |   /    1   \/ 10  |
x1 = -- - I*asinh|  /   - - + ------ |
     2           \\/      4     4    /

x_{1} = \frac{\pi}{2} - i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}

                 /     ______________\
                 |    /         ____ |
     pi          |   /    1   \/ 10  |
x2 = -- + I*asinh|  /   - - + ------ |
     2           \\/      4     4    /

x_{2} = \frac{\pi}{2} + i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}

                   /     ______________\
                   |    /         ____ |
     3*pi          |   /    1   \/ 10  |
x3 = ---- - I*asinh|  /   - - + ------ |
      2            \\/      4     4    /

x_{3} = \frac{3 \pi}{2} - i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}

                   /     ______________\
                   |    /         ____ |
     3*pi          |   /    1   \/ 10  |
x4 = ---- + I*asinh|  /   - - + ------ |
      2            \\/      4     4    /

x_{4} = \frac{3 \pi}{2} + i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}

         /    /      ____________\\              /    /      ____________\\
         |    |     /       ____ ||              |    |     /       ____ ||
         |    |    /  1   \/ 10  ||              |    |    /  1   \/ 10  ||
x5 = - re|acos|-  /   - + ------ || + 2*pi - I*im|acos|-  /   - + ------ ||
         \    \ \/    4     4    //              \    \ \/    4     4    //

x_{5} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}

                /    /     ____________\\
                |    |    /       ____ ||
                |    |   /  1   \/ 10  ||
x6 = 2*pi - I*im|acos|  /   - + ------ ||
                \    \\/    4     4    //

x_{6} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}

         /    /      ____________\\     /    /      ____________\\
         |    |     /       ____ ||     |    |     /       ____ ||
         |    |    /  1   \/ 10  ||     |    |    /  1   \/ 10  ||
x7 = I*im|acos|-  /   - + ------ || + re|acos|-  /   - + ------ ||
         \    \ \/    4     4    //     \    \ \/    4     4    //

x_{7} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}

         /    /     ____________\\     /    /     ____________\\
         |    |    /       ____ ||     |    |    /       ____ ||
         |    |   /  1   \/ 10  ||     |    |   /  1   \/ 10  ||
x8 = I*im|acos|  /   - + ------ || + re|acos|  /   - + ------ ||
         \    \\/    4     4    //     \    \\/    4     4    //

x_{8} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}

x8 = re(acos(sqrt(1/4 + sqrt(10)/4))) + i*im(acos(sqrt(1/4 + sqrt(10)/4)))

Suma y producto de raíces [src]

suma

            /     ______________\               /     ______________\                 /     ______________\                 /     ______________\       /    /      ____________\\              /    /      ____________\\              /    /     ____________\\       /    /      ____________\\     /    /      ____________\\       /    /     ____________\\     /    /     ____________\\
            |    /         ____ |               |    /         ____ |                 |    /         ____ |                 |    /         ____ |       |    |     /       ____ ||              |    |     /       ____ ||              |    |    /       ____ ||       |    |     /       ____ ||     |    |     /       ____ ||       |    |    /       ____ ||     |    |    /       ____ ||
pi          |   /    1   \/ 10  |   pi          |   /    1   \/ 10  |   3*pi          |   /    1   \/ 10  |   3*pi          |   /    1   \/ 10  |       |    |    /  1   \/ 10  ||              |    |    /  1   \/ 10  ||              |    |   /  1   \/ 10  ||       |    |    /  1   \/ 10  ||     |    |    /  1   \/ 10  ||       |    |   /  1   \/ 10  ||     |    |   /  1   \/ 10  ||
-- - I*asinh|  /   - - + ------ | + -- + I*asinh|  /   - - + ------ | + ---- - I*asinh|  /   - - + ------ | + ---- + I*asinh|  /   - - + ------ | + - re|acos|-  /   - + ------ || + 2*pi - I*im|acos|-  /   - + ------ || + 2*pi - I*im|acos|  /   - + ------ || + I*im|acos|-  /   - + ------ || + re|acos|-  /   - + ------ || + I*im|acos|  /   - + ------ || + re|acos|  /   - + ------ ||
2           \\/      4     4    /   2           \\/      4     4    /    2            \\/      4     4    /    2            \\/      4     4    /       \    \ \/    4     4    //              \    \ \/    4     4    //              \    \\/    4     4    //       \    \ \/    4     4    //     \    \ \/    4     4    //       \    \\/    4     4    //     \    \\/    4     4    //

\left(\left(\operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}\right) + \left(\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}\right) + \left(\left(\left(\left(\frac{3 \pi}{2} - i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right) + \left(\left(\frac{\pi}{2} - i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right) + \left(\frac{\pi}{2} + i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)\right)\right) + \left(\frac{3 \pi}{2} + i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}\right)\right)\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}\right)

         /    /     ____________\\
         |    |    /       ____ ||
         |    |   /  1   \/ 10  ||
8*pi + re|acos|  /   - + ------ ||
         \    \\/    4     4    //

\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)} + 8 \pi

producto

/            /     ______________\\ /            /     ______________\\ /              /     ______________\\ /              /     ______________\\ /    /    /      ____________\\              /    /      ____________\\\ /           /    /     ____________\\\ /    /    /      ____________\\     /    /      ____________\\\ /    /    /     ____________\\     /    /     ____________\\\
|            |    /         ____ || |            |    /         ____ || |              |    /         ____ || |              |    /         ____ || |    |    |     /       ____ ||              |    |     /       ____ ||| |           |    |    /       ____ ||| |    |    |     /       ____ ||     |    |     /       ____ ||| |    |    |    /       ____ ||     |    |    /       ____ |||
|pi          |   /    1   \/ 10  || |pi          |   /    1   \/ 10  || |3*pi          |   /    1   \/ 10  || |3*pi          |   /    1   \/ 10  || |    |    |    /  1   \/ 10  ||              |    |    /  1   \/ 10  ||| |           |    |   /  1   \/ 10  ||| |    |    |    /  1   \/ 10  ||     |    |    /  1   \/ 10  ||| |    |    |   /  1   \/ 10  ||     |    |   /  1   \/ 10  |||
|-- - I*asinh|  /   - - + ------ ||*|-- + I*asinh|  /   - - + ------ ||*|---- - I*asinh|  /   - - + ------ ||*|---- + I*asinh|  /   - - + ------ ||*|- re|acos|-  /   - + ------ || + 2*pi - I*im|acos|-  /   - + ------ |||*|2*pi - I*im|acos|  /   - + ------ |||*|I*im|acos|-  /   - + ------ || + re|acos|-  /   - + ------ |||*|I*im|acos|  /   - + ------ || + re|acos|  /   - + ------ |||
\2           \\/      4     4    // \2           \\/      4     4    // \ 2            \\/      4     4    // \ 2            \\/      4     4    // \    \    \ \/    4     4    //              \    \ \/    4     4    /// \           \    \\/    4     4    /// \    \    \ \/    4     4    //     \    \ \/    4     4    /// \    \    \\/    4     4    //     \    \\/    4     4    ///

\left(\frac{\pi}{2} - i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right) \left(\frac{\pi}{2} + i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right) \left(\frac{3 \pi}{2} - i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right) \left(\frac{3 \pi}{2} + i \operatorname{asinh}{\left(\sqrt{- \frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}\right) \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{\frac{1}{4} + \frac{\sqrt{10}}{4}} \right)}\right)}\right)

 /              /   _____________\\ /              /   _____________\\ /           /    /   ____________\\\ /                /   _____________\\ /                /   _____________\\ /    /    /   ____________\\     /    /   ____________\\\ /    /    /    ____________ \\     /    /    ____________ \\\ /            /    /    ____________ \\     /    /    ____________ \\\ 
 |              |  /        ____ || |              |  /        ____ || |           |    |  /       ____ ||| |                |  /        ____ || |                |  /        ____ || |    |    |  /       ____ ||     |    |  /       ____ ||| |    |    |   /       ____  ||     |    |   /       ____  ||| |            |    |   /       ____  ||     |    |   /       ____  ||| 
 |              |\/  -1 + \/ 10  || |              |\/  -1 + \/ 10  || |           |    |\/  1 + \/ 10  ||| |                |\/  -1 + \/ 10  || |                |\/  -1 + \/ 10  || |    |    |\/  1 + \/ 10  ||     |    |\/  1 + \/ 10  ||| |    |    |-\/  1 + \/ 10   ||     |    |-\/  1 + \/ 10   ||| |            |    |-\/  1 + \/ 10   ||     |    |-\/  1 + \/ 10   ||| 
-|pi - 2*I*asinh|----------------||*|pi + 2*I*asinh|----------------||*|2*pi - I*im|acos|---------------|||*|3*pi - 2*I*asinh|----------------||*|3*pi + 2*I*asinh|----------------||*|I*im|acos|---------------|| + re|acos|---------------|||*|I*im|acos|-----------------|| + re|acos|-----------------|||*|-2*pi + I*im|acos|-----------------|| + re|acos|-----------------||| 
 \              \       2        // \              \       2        // \           \    \       2       /// \                \       2        // \                \       2        // \    \    \       2       //     \    \       2       /// \    \    \        2        //     \    \        2        /// \            \    \        2        //     \    \        2        /// 
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                         16

- \frac{\left(\pi - 2 i \operatorname{asinh}{\left(\frac{\sqrt{-1 + \sqrt{10}}}{2} \right)}\right) \left(\pi + 2 i \operatorname{asinh}{\left(\frac{\sqrt{-1 + \sqrt{10}}}{2} \right)}\right) \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{\sqrt{1 + \sqrt{10}}}{2} \right)}\right)}\right) \left(3 \pi - 2 i \operatorname{asinh}{\left(\frac{\sqrt{-1 + \sqrt{10}}}{2} \right)}\right) \left(3 \pi + 2 i \operatorname{asinh}{\left(\frac{\sqrt{-1 + \sqrt{10}}}{2} \right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{\sqrt{1 + \sqrt{10}}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{\sqrt{1 + \sqrt{10}}}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{\sqrt{1 + \sqrt{10}}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{\sqrt{1 + \sqrt{10}}}{2} \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{\sqrt{1 + \sqrt{10}}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{\sqrt{1 + \sqrt{10}}}{2} \right)}\right)}\right)}{16}

-(pi - 2*i*asinh(sqrt(-1 + sqrt(10))/2))*(pi + 2*i*asinh(sqrt(-1 + sqrt(10))/2))*(2*pi - i*im(acos(sqrt(1 + sqrt(10))/2)))*(3*pi - 2*i*asinh(sqrt(-1 + sqrt(10))/2))*(3*pi + 2*i*asinh(sqrt(-1 + sqrt(10))/2))*(i*im(acos(sqrt(1 + sqrt(10))/2)) + re(acos(sqrt(1 + sqrt(10))/2)))*(i*im(acos(-sqrt(1 + sqrt(10))/2)) + re(acos(-sqrt(1 + sqrt(10))/2)))*(-2*pi + i*im(acos(-sqrt(1 + sqrt(10))/2)) + re(acos(-sqrt(1 + sqrt(10))/2)))/16

Respuesta numérica [src]

x1 = 1.5707963267949 - 0.681292706039573*i

x2 = 1.5707963267949 + 0.681292706039573*i

x3 = 4.71238898038469 - 0.681292706039573*i

x4 = 4.71238898038469 + 0.681292706039573*i

x5 = 3.14159265358979 + 0.20008088097997*i

x6 = 6.28318530717959 - 0.20008088097997*i

x7 = 3.14159265358979 - 0.20008088097997*i

x8 = 0.20008088097997*i

x8 = 0.20008088097997*i

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Expresiones idénticas

Expresiones semejantes

8cos^2(x)(2cos^2(x)-1)=9 la ecuación

Solución numérica:

Solución