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La ecuación:
Ecuación 8*x-3*(2*x+1)=2*x+4
Ecuación x^3=27
Ecuación 1+sin(x)=0
Ecuación 2*x^2+6*x+9=
Expresar {x} en función de y en la ecuación:
20*x+6*y=8
-11*x-15*y=14
-11*x+10*y=-9
6*x-2*y=20
Expresiones idénticas
(4sin^ dos (x/ tres)- uno dos sin(x/ tres)+ nueve)^(uno / dos)+((dos sin(x/ tres)- cinco)^ dos)^(uno / dos)= ocho -2* tres ^(1/2)
(4 seno de al cuadrado (x dividir por 3) menos 12 seno de (x dividir por 3) más 9) en el grado (1 dividir por 2) más ((2 seno de (x dividir por 3) menos 5) al cuadrado ) en el grado (1 dividir por 2) es igual a 8 menos 2 multiplicar por 3 en el grado (1 dividir por 2)
(4 seno de en el grado dos (x dividir por tres) menos uno dos seno de (x dividir por tres) más nueve) en el grado (uno dividir por dos) más ((dos seno de (x dividir por tres) menos cinco) en el grado dos) en el grado (uno dividir por dos) es igual a ocho menos 2 multiplicar por tres en el grado (1 dividir por 2)
(4sin2(x/3)-12sin(x/3)+9)(1/2)+((2sin(x/3)-5)2)(1/2)=8-2*3(1/2)
4sin2x/3-12sinx/3+91/2+2sinx/3-521/2=8-2*31/2
(4sin²(x/3)-12sin(x/3)+9)^(1/2)+((2sin(x/3)-5)²)^(1/2)=8-2*3^(1/2)
(4sin en el grado 2(x/3)-12sin(x/3)+9) en el grado (1/2)+((2sin(x/3)-5) en el grado 2) en el grado (1/2)=8-2*3 en el grado (1/2)
(4sin^2(x/3)-12sin(x/3)+9)^(1/2)+((2sin(x/3)-5)^2)^(1/2)=8-23^(1/2)
(4sin2(x/3)-12sin(x/3)+9)(1/2)+((2sin(x/3)-5)2)(1/2)=8-23(1/2)
4sin2x/3-12sinx/3+91/2+2sinx/3-521/2=8-231/2
4sin^2x/3-12sinx/3+9^1/2+2sinx/3-5^2^1/2=8-23^1/2
(4sin^2(x dividir por 3)-12sin(x dividir por 3)+9)^(1 dividir por 2)+((2sin(x dividir por 3)-5)^2)^(1 dividir por 2)=8-2*3^(1 dividir por 2)
Expresiones semejantes
(4sin^2(x/3)-12sin(x/3)+9)^(1/2)-((2sin(x/3)-5)^2)^(1/2)=8-2*3^(1/2)
(4sin^2(x/3)-12sin(x/3)-9)^(1/2)+((2sin(x/3)-5)^2)^(1/2)=8-2*3^(1/2)
(4sin^2(x/3)-12sin(x/3)+9)^(1/2)+((2sin(x/3)+5)^2)^(1/2)=8-2*3^(1/2)
(4sin^2(x/3)-12sin(x/3)+9)^(1/2)+((2sin(x/3)-5)^2)^(1/2)=8+2*3^(1/2)
(4sin^2(x/3)+12sin(x/3)+9)^(1/2)+((2sin(x/3)-5)^2)^(1/2)=8-2*3^(1/2)

(4sin^2(x/3)-12sin(x/3)+9)^(1/2)+((2sin(x/3)-5)^2)^(1/2)=8-2*3^(1/2) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

                                       _________________              
    ___________________________       /               2               
   /      2/x\         /x\           /  /     /x\    \             ___
  /  4*sin |-| - 12*sin|-| + 9  +   /   |2*sin|-| - 5|   = 8 - 2*\/ 3 
\/         \3/         \3/        \/    \     \3/    /

$$\sqrt{\left(4 \sin^{2}{\left(\frac{x}{3} \right)} - 12 \sin{\left(\frac{x}{3} \right)}\right) + 9} + \sqrt{\left(2 \sin{\left(\frac{x}{3} \right)} - 5\right)^{2}} = 8 - 2 \sqrt{3}$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

x1 = pi

$$x_{1} = \pi$$

           /    /             __________________\\                /    /             __________________\\
           |    |      ___   /              ___ ||                |    |      ___   /              ___ ||
           |    |    \/ 3 *\/  1393 - 800*\/ 3  ||                |    |    \/ 3 *\/  1393 - 800*\/ 3  ||
x2 = - 3*re|asin|2 + ---------------------------|| + 3*pi - 3*I*im|asin|2 + ---------------------------||
           |    |            /        ___\      ||                |    |            /        ___\      ||
           \    \          2*\9 - 4*\/ 3 /      //                \    \          2*\9 - 4*\/ 3 /      //

$$x_{2} = - 3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)} + 3 \pi - 3 i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)}$$

             /             __________________\       
             |      ___   /              ___ |       
             |    \/ 3 *\/  1393 - 800*\/ 3  |       
x3 = - 3*asin|2 - ---------------------------| + 3*pi
             |            /        ___\      |       
             \          2*\9 - 4*\/ 3 /      /

$$x_{3} = - 3 \operatorname{asin}{\left(- \frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)} + 3 \pi$$

           /             __________________\
           |      ___   /              ___ |
           |    \/ 3 *\/  1393 - 800*\/ 3  |
x4 = 3*asin|2 - ---------------------------|
           |            /        ___\      |
           \          2*\9 - 4*\/ 3 /      /

$$x_{4} = 3 \operatorname{asin}{\left(- \frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}$$

         /    /             __________________\\         /    /             __________________\\
         |    |      ___   /              ___ ||         |    |      ___   /              ___ ||
         |    |    \/ 3 *\/  1393 - 800*\/ 3  ||         |    |    \/ 3 *\/  1393 - 800*\/ 3  ||
x5 = 3*re|asin|2 + ---------------------------|| + 3*I*im|asin|2 + ---------------------------||
         |    |            /        ___\      ||         |    |            /        ___\      ||
         \    \          2*\9 - 4*\/ 3 /      //         \    \          2*\9 - 4*\/ 3 /      //

$$x_{5} = 3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)} + 3 i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)}$$

x5 = 3*re(asin(sqrt(3)*sqrt(1393 - 800*sqrt(3))/(2*(9 - 4*sqrt(3))) + 2)) + 3*i*im(asin(sqrt(3)*sqrt(1393 - 800*sqrt(3))/(2*(9 - 4*sqrt(3))) + 2))

Suma y producto de raíces [src]

suma

           /    /             __________________\\                /    /             __________________\\           /             __________________\                /             __________________\       /    /             __________________\\         /    /             __________________\\
           |    |      ___   /              ___ ||                |    |      ___   /              ___ ||           |      ___   /              ___ |                |      ___   /              ___ |       |    |      ___   /              ___ ||         |    |      ___   /              ___ ||
           |    |    \/ 3 *\/  1393 - 800*\/ 3  ||                |    |    \/ 3 *\/  1393 - 800*\/ 3  ||           |    \/ 3 *\/  1393 - 800*\/ 3  |                |    \/ 3 *\/  1393 - 800*\/ 3  |       |    |    \/ 3 *\/  1393 - 800*\/ 3  ||         |    |    \/ 3 *\/  1393 - 800*\/ 3  ||
pi + - 3*re|asin|2 + ---------------------------|| + 3*pi - 3*I*im|asin|2 + ---------------------------|| + - 3*asin|2 - ---------------------------| + 3*pi + 3*asin|2 - ---------------------------| + 3*re|asin|2 + ---------------------------|| + 3*I*im|asin|2 + ---------------------------||
           |    |            /        ___\      ||                |    |            /        ___\      ||           |            /        ___\      |                |            /        ___\      |       |    |            /        ___\      ||         |    |            /        ___\      ||
           \    \          2*\9 - 4*\/ 3 /      //                \    \          2*\9 - 4*\/ 3 /      //           \          2*\9 - 4*\/ 3 /      /                \          2*\9 - 4*\/ 3 /      /       \    \          2*\9 - 4*\/ 3 /      //         \    \          2*\9 - 4*\/ 3 /      //

$$\left(3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)} + 3 i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)}\right) + \left(3 \operatorname{asin}{\left(- \frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)} + \left(\left(- 3 \operatorname{asin}{\left(- \frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)} + 3 \pi\right) + \left(\pi + \left(- 3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)} + 3 \pi - 3 i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)}\right)\right)\right)\right)$$

7*pi

$$7 \pi$$

producto

   /      /    /             __________________\\                /    /             __________________\\\ /        /             __________________\       \       /             __________________\ /    /    /             __________________\\         /    /             __________________\\\
   |      |    |      ___   /              ___ ||                |    |      ___   /              ___ ||| |        |      ___   /              ___ |       |       |      ___   /              ___ | |    |    |      ___   /              ___ ||         |    |      ___   /              ___ |||
   |      |    |    \/ 3 *\/  1393 - 800*\/ 3  ||                |    |    \/ 3 *\/  1393 - 800*\/ 3  ||| |        |    \/ 3 *\/  1393 - 800*\/ 3  |       |       |    \/ 3 *\/  1393 - 800*\/ 3  | |    |    |    \/ 3 *\/  1393 - 800*\/ 3  ||         |    |    \/ 3 *\/  1393 - 800*\/ 3  |||
pi*|- 3*re|asin|2 + ---------------------------|| + 3*pi - 3*I*im|asin|2 + ---------------------------|||*|- 3*asin|2 - ---------------------------| + 3*pi|*3*asin|2 - ---------------------------|*|3*re|asin|2 + ---------------------------|| + 3*I*im|asin|2 + ---------------------------|||
   |      |    |            /        ___\      ||                |    |            /        ___\      ||| |        |            /        ___\      |       |       |            /        ___\      | |    |    |            /        ___\      ||         |    |            /        ___\      |||
   \      \    \          2*\9 - 4*\/ 3 /      //                \    \          2*\9 - 4*\/ 3 /      /// \        \          2*\9 - 4*\/ 3 /      /       /       \          2*\9 - 4*\/ 3 /      / \    \    \          2*\9 - 4*\/ 3 /      //         \    \          2*\9 - 4*\/ 3 /      ///

$$\pi \left(- 3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)} + 3 \pi - 3 i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)}\right) \left(- 3 \operatorname{asin}{\left(- \frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)} + 3 \pi\right) 3 \operatorname{asin}{\left(- \frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)} \left(3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)} + 3 i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{2 \left(9 - 4 \sqrt{3}\right)} + 2 \right)}\right)}\right)$$

      /         /          __________________              __________________\\ /    /    /         __________________              __________________\\     /    /         __________________              __________________\\\ /          /    /         __________________              __________________\\     /    /         __________________              __________________\\\     /          __________________              __________________\
      |         |         /              ___        ___   /              ___ || |    |    |        /              ___        ___   /              ___ ||     |    |        /              ___        ___   /              ___ ||| |          |    |        /              ___        ___   /              ___ ||     |    |        /              ___        ___   /              ___ |||     |         /              ___        ___   /              ___ |
      |         |     2*\/  1393 - 800*\/ 3     3*\/ 3 *\/  1393 - 800*\/ 3  || |    |    |    2*\/  1393 - 800*\/ 3     3*\/ 3 *\/  1393 - 800*\/ 3  ||     |    |    2*\/  1393 - 800*\/ 3     3*\/ 3 *\/  1393 - 800*\/ 3  ||| |          |    |    2*\/  1393 - 800*\/ 3     3*\/ 3 *\/  1393 - 800*\/ 3  ||     |    |    2*\/  1393 - 800*\/ 3     3*\/ 3 *\/  1393 - 800*\/ 3  |||     |     2*\/  1393 - 800*\/ 3     3*\/ 3 *\/  1393 - 800*\/ 3  |
81*pi*|pi + asin|-2 + ----------------------- + -----------------------------||*|I*im|asin|2 + ----------------------- + -----------------------------|| + re|asin|2 + ----------------------- + -----------------------------|||*|-pi + I*im|asin|2 + ----------------------- + -----------------------------|| + re|asin|2 + ----------------------- + -----------------------------|||*asin|-2 + ----------------------- + -----------------------------|
      \         \                11                           22             // \    \    \               11                           22             //     \    \               11                           22             /// \          \    \               11                           22             //     \    \               11                           22             ///     \                11                           22             /

$$81 \pi \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{2 \sqrt{1393 - 800 \sqrt{3}}}{11} + \frac{3 \sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{22} + 2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2 \sqrt{1393 - 800 \sqrt{3}}}{11} + \frac{3 \sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{22} + 2 \right)}\right)}\right) \left(\operatorname{asin}{\left(-2 + \frac{2 \sqrt{1393 - 800 \sqrt{3}}}{11} + \frac{3 \sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{22} \right)} + \pi\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{2 \sqrt{1393 - 800 \sqrt{3}}}{11} + \frac{3 \sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{22} + 2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2 \sqrt{1393 - 800 \sqrt{3}}}{11} + \frac{3 \sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{22} + 2 \right)}\right)}\right) \operatorname{asin}{\left(-2 + \frac{2 \sqrt{1393 - 800 \sqrt{3}}}{11} + \frac{3 \sqrt{3} \sqrt{1393 - 800 \sqrt{3}}}{22} \right)}$$

81*pi*(pi + asin(-2 + 2*sqrt(1393 - 800*sqrt(3))/11 + 3*sqrt(3)*sqrt(1393 - 800*sqrt(3))/22))*(i*im(asin(2 + 2*sqrt(1393 - 800*sqrt(3))/11 + 3*sqrt(3)*sqrt(1393 - 800*sqrt(3))/22)) + re(asin(2 + 2*sqrt(1393 - 800*sqrt(3))/11 + 3*sqrt(3)*sqrt(1393 - 800*sqrt(3))/22)))*(-pi + i*im(asin(2 + 2*sqrt(1393 - 800*sqrt(3))/11 + 3*sqrt(3)*sqrt(1393 - 800*sqrt(3))/22)) + re(asin(2 + 2*sqrt(1393 - 800*sqrt(3))/11 + 3*sqrt(3)*sqrt(1393 - 800*sqrt(3))/22)))*asin(-2 + 2*sqrt(1393 - 800*sqrt(3))/11 + 3*sqrt(3)*sqrt(1393 - 800*sqrt(3))/22)

Respuesta numérica [src]

x1 = 17910.2197181154

x2 = 43.9822971502571

x3 = -72.2566310325652

x4 = 81.6814089933346

x5 = -31.4159265358979

x6 = 97.3893722612836

x7 = -295.309709437441

x8 = 3.14159265358979

x9 = 6.28318530717959

x10 = -50.2654824574367

x11 = -91.106186954104

x12 = -69.1150383789755

x13 = 135.088484104361

x14 = -87.9645943005142

x15 = 40.8407044966673

x16 = 100.530964914873

x17 = 62.8318530717959

x18 = -53.4070751110265

x19 = 21.9911485751286

x20 = -15.707963267949

x21 = 59.6902604182061

x22 = 116.238928182822

x23 = -12.5663706143592

x24 = 78.5398163397448

x25 = 25.1327412287183

x26 = -34.5575191894877

x26 = -34.5575191894877

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Expresiones idénticas

Expresiones semejantes

(4sin^2(x/3)-12sin(x/3)+9)^(1/2)+((2sin(x/3)-5)^2)^(1/2)=8-2*3^(1/2) la ecuación

Solución numérica:

Solución