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La ecuación:
Ecuación 3^x=27
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
Ecuación x(x^2+2x+1)=6(x+1)
Ecuación 4x+1=-3x+15
Expresar {x} en función de y en la ecuación:
-6*x-20*y=8
7*x-1*y=0
2*x-8*y=4
2*x-15*y=-1
Expresiones idénticas
√(cuatro cos^ dos (x))+√(4sin^ dos (x)+ uno)=4
√(4 coseno de al cuadrado (x)) más √(4 seno de al cuadrado (x) más 1) es igual a 4
√(cuatro coseno de en el grado dos (x)) más √(4 seno de en el grado dos (x) más uno) es igual a 4
√(4cos2(x))+√(4sin2(x)+1)=4
√4cos2x+√4sin2x+1=4
√(4cos²(x))+√(4sin²(x)+1)=4
√(4cos en el grado 2(x))+√(4sin en el grado 2(x)+1)=4
√4cos^2x+√4sin^2x+1=4
Expresiones semejantes
√(4cos^2(x))-√(4sin^2(x)+1)=4
√(4cos^2(x))+√(4sin^2(x)-1)=4

√(4cos^2(x))+√(4sin^2(x)+1)=4 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

   ___________      _______________    
  /      2         /      2            
\/  4*cos (x)  + \/  4*sin (x) + 1  = 4

\sqrt{4 \sin^{2}{\left(x \right)} + 1} + \sqrt{4 \cos^{2}{\left(x \right)}} = 4

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

         //       /         ________________\         /      /         ________________\\    \     //       /         ________________\         /      /         ________________\\    \
         ||       |  ___   /            ___ |         |      |  ___   /            ___ ||    |     ||       |  ___   /            ___ |         |      |  ___   /            ___ ||    |
         ||       |\/ 3 *\/  -3 - 4*I*\/ 6  |         |      |\/ 3 *\/  -3 - 4*I*\/ 6  ||    |     ||       |\/ 3 *\/  -3 - 4*I*\/ 6  |         |      |\/ 3 *\/  -3 - 4*I*\/ 6  ||    |
x1 = I*im|<-2*atan|-------------------------|  for cos|2*atan|-------------------------|| < 0| + re|<-2*atan|-------------------------|  for cos|2*atan|-------------------------|| < 0|
         ||       \            3            /         \      \            3            //    |     ||       \            3            /         \      \            3            //    |
         ||                                                                                  |     ||                                                                                  |
         \\               nan                                    otherwise                   /     \\               nan                                    otherwise                   /

x_{1} = \operatorname{re}{\left(\begin{cases} - 2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 - 4 \sqrt{6} i}}{3} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 - 4 \sqrt{6} i}}{3} \right)} \right)} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - 2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 - 4 \sqrt{6} i}}{3} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 - 4 \sqrt{6} i}}{3} \right)} \right)} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

         //      /         ________________\         /      /         ________________\\    \     //      /         ________________\         /      /         ________________\\    \
         ||      |  ___   /            ___ |         |      |  ___   /            ___ ||    |     ||      |  ___   /            ___ |         |      |  ___   /            ___ ||    |
         ||      |\/ 3 *\/  -3 - 4*I*\/ 6  |         |      |\/ 3 *\/  -3 - 4*I*\/ 6  ||    |     ||      |\/ 3 *\/  -3 - 4*I*\/ 6  |         |      |\/ 3 *\/  -3 - 4*I*\/ 6  ||    |
x2 = I*im|<2*atan|-------------------------|  for cos|2*atan|-------------------------|| < 0| + re|<2*atan|-------------------------|  for cos|2*atan|-------------------------|| < 0|
         ||      \            3            /         \      \            3            //    |     ||      \            3            /         \      \            3            //    |
         ||                                                                                 |     ||                                                                                 |
         \\               nan                                   otherwise                   /     \\               nan                                   otherwise                   /

x_{2} = \operatorname{re}{\left(\begin{cases} 2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 - 4 \sqrt{6} i}}{3} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 - 4 \sqrt{6} i}}{3} \right)} \right)} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 - 4 \sqrt{6} i}}{3} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 - 4 \sqrt{6} i}}{3} \right)} \right)} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

         //       /         ________________\         /      /         ________________\\    \     //       /         ________________\         /      /         ________________\\    \
         ||       |  ___   /            ___ |         |      |  ___   /            ___ ||    |     ||       |  ___   /            ___ |         |      |  ___   /            ___ ||    |
         ||       |\/ 3 *\/  -3 + 4*I*\/ 6  |         |      |\/ 3 *\/  -3 + 4*I*\/ 6  ||    |     ||       |\/ 3 *\/  -3 + 4*I*\/ 6  |         |      |\/ 3 *\/  -3 + 4*I*\/ 6  ||    |
x3 = I*im|<-2*atan|-------------------------|  for cos|2*atan|-------------------------|| < 0| + re|<-2*atan|-------------------------|  for cos|2*atan|-------------------------|| < 0|
         ||       \            3            /         \      \            3            //    |     ||       \            3            /         \      \            3            //    |
         ||                                                                                  |     ||                                                                                  |
         \\               nan                                    otherwise                   /     \\               nan                                    otherwise                   /

x_{3} = \operatorname{re}{\left(\begin{cases} - 2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 + 4 \sqrt{6} i}}{3} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 + 4 \sqrt{6} i}}{3} \right)} \right)} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - 2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 + 4 \sqrt{6} i}}{3} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 + 4 \sqrt{6} i}}{3} \right)} \right)} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

         //      /         ________________\         /      /         ________________\\    \     //      /         ________________\         /      /         ________________\\    \
         ||      |  ___   /            ___ |         |      |  ___   /            ___ ||    |     ||      |  ___   /            ___ |         |      |  ___   /            ___ ||    |
         ||      |\/ 3 *\/  -3 + 4*I*\/ 6  |         |      |\/ 3 *\/  -3 + 4*I*\/ 6  ||    |     ||      |\/ 3 *\/  -3 + 4*I*\/ 6  |         |      |\/ 3 *\/  -3 + 4*I*\/ 6  ||    |
x4 = I*im|<2*atan|-------------------------|  for cos|2*atan|-------------------------|| < 0| + re|<2*atan|-------------------------|  for cos|2*atan|-------------------------|| < 0|
         ||      \            3            /         \      \            3            //    |     ||      \            3            /         \      \            3            //    |
         ||                                                                                 |     ||                                                                                 |
         \\               nan                                   otherwise                   /     \\               nan                                   otherwise                   /

x_{4} = \operatorname{re}{\left(\begin{cases} 2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 + 4 \sqrt{6} i}}{3} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 + 4 \sqrt{6} i}}{3} \right)} \right)} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 + 4 \sqrt{6} i}}{3} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-3 + 4 \sqrt{6} i}}{3} \right)} \right)} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

         //       /          ________________\         /      /          ________________\\     \     //       /          ________________\         /      /          ________________\\     \
         ||       |  ____   /            ___ |         |      |  ____   /            ___ ||     |     ||       |  ____   /            ___ |         |      |  ____   /            ___ ||     |
         ||       |\/ 35 *\/  -3 - 4*I*\/ 6  |         |      |\/ 35 *\/  -3 - 4*I*\/ 6  ||     |     ||       |\/ 35 *\/  -3 - 4*I*\/ 6  |         |      |\/ 35 *\/  -3 - 4*I*\/ 6  ||     |
x5 = I*im|<-2*atan|--------------------------|  for cos|2*atan|--------------------------|| >= 0| + re|<-2*atan|--------------------------|  for cos|2*atan|--------------------------|| >= 0|
         ||       \            35            /         \      \            35            //     |     ||       \            35            /         \      \            35            //     |
         ||                                                                                     |     ||                                                                                     |
         \\                nan                                     otherwise                    /     \\                nan                                     otherwise                    /

x_{5} = \operatorname{re}{\left(\begin{cases} - 2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)} \right)} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - 2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)} \right)} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

         //      /          ________________\         /      /          ________________\\     \     //      /          ________________\         /      /          ________________\\     \
         ||      |  ____   /            ___ |         |      |  ____   /            ___ ||     |     ||      |  ____   /            ___ |         |      |  ____   /            ___ ||     |
         ||      |\/ 35 *\/  -3 - 4*I*\/ 6  |         |      |\/ 35 *\/  -3 - 4*I*\/ 6  ||     |     ||      |\/ 35 *\/  -3 - 4*I*\/ 6  |         |      |\/ 35 *\/  -3 - 4*I*\/ 6  ||     |
x6 = I*im|<2*atan|--------------------------|  for cos|2*atan|--------------------------|| >= 0| + re|<2*atan|--------------------------|  for cos|2*atan|--------------------------|| >= 0|
         ||      \            35            /         \      \            35            //     |     ||      \            35            /         \      \            35            //     |
         ||                                                                                    |     ||                                                                                    |
         \\               nan                                     otherwise                    /     \\               nan                                     otherwise                    /

x_{6} = \operatorname{re}{\left(\begin{cases} 2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)} \right)} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)} \right)} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

         //       /          ________________\         /      /          ________________\\     \     //       /          ________________\         /      /          ________________\\     \
         ||       |  ____   /            ___ |         |      |  ____   /            ___ ||     |     ||       |  ____   /            ___ |         |      |  ____   /            ___ ||     |
         ||       |\/ 35 *\/  -3 + 4*I*\/ 6  |         |      |\/ 35 *\/  -3 + 4*I*\/ 6  ||     |     ||       |\/ 35 *\/  -3 + 4*I*\/ 6  |         |      |\/ 35 *\/  -3 + 4*I*\/ 6  ||     |
x7 = I*im|<-2*atan|--------------------------|  for cos|2*atan|--------------------------|| >= 0| + re|<-2*atan|--------------------------|  for cos|2*atan|--------------------------|| >= 0|
         ||       \            35            /         \      \            35            //     |     ||       \            35            /         \      \            35            //     |
         ||                                                                                     |     ||                                                                                     |
         \\                nan                                     otherwise                    /     \\                nan                                     otherwise                    /

x_{7} = \operatorname{re}{\left(\begin{cases} - 2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)} \right)} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - 2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)} \right)} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

         //      /          ________________\         /      /          ________________\\     \     //      /          ________________\         /      /          ________________\\     \
         ||      |  ____   /            ___ |         |      |  ____   /            ___ ||     |     ||      |  ____   /            ___ |         |      |  ____   /            ___ ||     |
         ||      |\/ 35 *\/  -3 + 4*I*\/ 6  |         |      |\/ 35 *\/  -3 + 4*I*\/ 6  ||     |     ||      |\/ 35 *\/  -3 + 4*I*\/ 6  |         |      |\/ 35 *\/  -3 + 4*I*\/ 6  ||     |
x8 = I*im|<2*atan|--------------------------|  for cos|2*atan|--------------------------|| >= 0| + re|<2*atan|--------------------------|  for cos|2*atan|--------------------------|| >= 0|
         ||      \            35            /         \      \            35            //     |     ||      \            35            /         \      \            35            //     |
         ||                                                                                    |     ||                                                                                    |
         \\               nan                                     otherwise                    /     \\               nan                                     otherwise                    /

x_{8} = \operatorname{re}{\left(\begin{cases} 2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)} \right)} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)} & \text{for}\: \cos{\left(2 \operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)} \right)} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

           /    /          ________________\\         /    /          ________________\\
           |    |  ____   /            ___ ||         |    |  ____   /            ___ ||
           |    |\/ 35 *\/  -3 - 4*I*\/ 6  ||         |    |\/ 35 *\/  -3 - 4*I*\/ 6  ||
x9 = - 2*re|atan|--------------------------|| - 2*I*im|atan|--------------------------||
           \    \            35            //         \    \            35            //

x_{9} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)}\right)}

          /    /          ________________\\         /    /          ________________\\
          |    |  ____   /            ___ ||         |    |  ____   /            ___ ||
          |    |\/ 35 *\/  -3 - 4*I*\/ 6  ||         |    |\/ 35 *\/  -3 - 4*I*\/ 6  ||
x10 = 2*re|atan|--------------------------|| + 2*I*im|atan|--------------------------||
          \    \            35            //         \    \            35            //

x_{10} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 - 4 \sqrt{6} i}}{35} \right)}\right)}

            /    /          ________________\\         /    /          ________________\\
            |    |  ____   /            ___ ||         |    |  ____   /            ___ ||
            |    |\/ 35 *\/  -3 + 4*I*\/ 6  ||         |    |\/ 35 *\/  -3 + 4*I*\/ 6  ||
x11 = - 2*re|atan|--------------------------|| - 2*I*im|atan|--------------------------||
            \    \            35            //         \    \            35            //

x_{11} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)}\right)}

          /    /          ________________\\         /    /          ________________\\
          |    |  ____   /            ___ ||         |    |  ____   /            ___ ||
          |    |\/ 35 *\/  -3 + 4*I*\/ 6  ||         |    |\/ 35 *\/  -3 + 4*I*\/ 6  ||
x12 = 2*re|atan|--------------------------|| + 2*I*im|atan|--------------------------||
          \    \            35            //         \    \            35            //

x_{12} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{35} \sqrt{-3 + 4 \sqrt{6} i}}{35} \right)}\right)}

x12 = 2*re(atan(sqrt(35)*sqrt(-3 + 4*sqrt(6)*i)/35)) + 2*i*im(atan(sqrt(35)*sqrt(-3 + 4*sqrt(6)*i)/35))

Respuesta numérica [src]

x1 = -0.738262802202509 + 0.816214129514672*i

x2 = 0.738262802202509 - 0.816214129514672*i

x3 = -0.738262802202509 - 0.816214129514672*i

x4 = 0.738262802202509 + 0.816214129514672*i

x4 = 0.738262802202509 + 0.816214129514672*i

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√(4cos^2(x))+√(4sin^2(x)+1)=4 la ecuación

Solución numérica:

Solución