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- La ecuación:
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Ecuación x^3-x^2-x-1=0
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Ecuación 3x-2(3x+4)=10
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Ecuación 12-4(x-3)=39-9x
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Ecuación 0,2x+2,7=1,4-1,1x
- Expresar {x} en función de y en la ecuación:
- -11*x-3*y=14
- 2*x-15*y=-1
- -18*x-6*y=-1
- 6*x+9*y=-9
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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
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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
$$\sqrt{4 \sin^{2}{\left(x \right)} + 1} + \sqrt{4 \cos^{2}{\left(x \right)}} = 4$$
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
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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