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- La ecuación:
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Ecuación x^2+11=0
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Ecuación 3x-2(3x+4)=10
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Ecuación 1/x^2-3/x-4=0
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Ecuación x(x^2+2x+1)=6(x+1)
- Expresar {x} en función de y en la ecuación:
- 7*x-1*y=0
- -11*x-3*y=14
- 2*x-15*y=-1
- -18*x-6*y=-1
- Suma de la serie:
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1,54
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Expresiones idénticas
- 2sinx*cosx= uno , cincuenta y cuatro
- 2 seno de x multiplicar por coseno de x es igual a 1,54
- 2 seno de x multiplicar por coseno de x es igual a uno , cincuenta y cuatro
- 2sinxcosx=1,54
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Expresiones semejantes
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- x*12+x*1,5*4=131000
- (1+h1)^4*(1+h1/1,5)^4-1,21=0
- (cos(x)-sin(x))*(1-2*sin(x)*cos(x))+1=0
- 2*sin(x)*cos(x)=1/2
- -4,6-1,5(4x-5)+8,5x=0.3(3x-7)+(2x-15.6)/7
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Expresiones con funciones
- cosx
- cosx+sinx=sqrt2*sin(2x)
- cosx=8^(-1/6)
- cosx⋅ctgx−(−√3/3)cosx=0
- Cosxcos2x-sin2xx=-1
- cosx/(sinx-1)=0
2sinx*cosx=1,54 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
77
2*sin(x)*cos(x) = --
50
$$2 \sin{\left(x \right)} \cos{\left(x \right)} = \frac{77}{50}$$
Respuesta rápida
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/ / __________________ \\ / / __________________ \\
| | / _____ _____|| | | / _____ _____||
| | 50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | | 50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 ||
x1 = 2*re|atan|- -- + ------------------------ + -----------|| + 2*I*im|atan|- -- + ------------------------ + -----------||
\ \ 77 77 77 // \ \ 77 77 77 //
$$x_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{50}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{50}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}$$
/ / __________________ \\ / / __________________ \\
| | / _____ _____|| | | / _____ _____||
| |50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 ||
x2 = - 2*re|atan|-- + ------------------------ - -----------|| - 2*I*im|atan|-- + ------------------------ - -----------||
\ \77 77 77 // \ \77 77 77 //
$$x_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{3 \sqrt{381} i}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{3 \sqrt{381} i}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} \right)}\right)}$$
/ / __________________ \\ / / __________________ \\
| | / _____ _____|| | | / _____ _____||
| |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 ||
x3 = - 2*re|atan|-- - ------------------------ + -----------|| - 2*I*im|atan|-- - ------------------------ + -----------||
\ \77 77 77 // \ \77 77 77 //
$$x_{3} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}$$
/ / __________________ \\ / / __________________ \\
| | / _____ _____|| | | / _____ _____||
| |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 ||
x4 = - 2*re|atan|-- + ------------------------ + -----------|| - 2*I*im|atan|-- + ------------------------ + -----------||
\ \77 77 77 // \ \77 77 77 //
$$x_{4} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} + \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} + \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}$$
x4 = -2*re(atan(50/77 + 10*sqrt(50 + 3*sqrt(381)*i)/77 + 3*sqrt(381)*i/77)) - 2*i*im(atan(50/77 + 10*sqrt(50 + 3*sqrt(381)*i)/77 + 3*sqrt(381)*i/77))
Suma y producto de raíces
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suma
/ / __________________ \\ / / __________________ \\ / / __________________ \\ / / __________________ \\ / / __________________ \\ / / __________________ \\ / / __________________ \\ / / __________________ \\
| | / _____ _____|| | | / _____ _____|| | | / _____ _____|| | | / _____ _____|| | | / _____ _____|| | | / _____ _____|| | | / _____ _____|| | | / _____ _____||
| | 50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | | 50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 ||
2*re|atan|- -- + ------------------------ + -----------|| + 2*I*im|atan|- -- + ------------------------ + -----------|| + - 2*re|atan|-- + ------------------------ - -----------|| - 2*I*im|atan|-- + ------------------------ - -----------|| + - 2*re|atan|-- - ------------------------ + -----------|| - 2*I*im|atan|-- - ------------------------ + -----------|| + - 2*re|atan|-- + ------------------------ + -----------|| - 2*I*im|atan|-- + ------------------------ + -----------||
\ \ 77 77 77 // \ \ 77 77 77 // \ \77 77 77 // \ \77 77 77 // \ \77 77 77 // \ \77 77 77 // \ \77 77 77 // \ \77 77 77 //
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} + \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} + \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}\right) + \left(\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}\right) + \left(\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{3 \sqrt{381} i}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{3 \sqrt{381} i}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{50}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{50}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}\right)\right)\right)$$
=
/ / __________________ \\ / / __________________ \\ / / __________________ \\ / / __________________ \\ / / __________________ \\ / / __________________ \\ / / __________________ \\ / / __________________ \\
| | / _____ _____|| | | / _____ _____|| | | / _____ _____|| | | / _____ _____|| | | / _____ _____|| | | / _____ _____|| | | / _____ _____|| | | / _____ _____||
| |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | | 50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | | 50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 ||
- 2*re|atan|-- - ------------------------ + -----------|| - 2*re|atan|-- + ------------------------ - -----------|| - 2*re|atan|-- + ------------------------ + -----------|| + 2*re|atan|- -- + ------------------------ + -----------|| - 2*I*im|atan|-- - ------------------------ + -----------|| - 2*I*im|atan|-- + ------------------------ - -----------|| - 2*I*im|atan|-- + ------------------------ + -----------|| + 2*I*im|atan|- -- + ------------------------ + -----------||
\ \77 77 77 // \ \77 77 77 // \ \77 77 77 // \ \ 77 77 77 // \ \77 77 77 // \ \77 77 77 // \ \77 77 77 // \ \ 77 77 77 //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{3 \sqrt{381} i}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} + \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{50}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} + \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{3 \sqrt{381} i}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{50}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}$$
producto
/ / / __________________ \\ / / __________________ \\\ / / / __________________ \\ / / __________________ \\\ / / / __________________ \\ / / __________________ \\\ / / / __________________ \\ / / __________________ \\\ | | | / _____ _____|| | | / _____ _____||| | | | / _____ _____|| | | / _____ _____||| | | | / _____ _____|| | | / _____ _____||| | | | / _____ _____|| | | / _____ _____||| | | | 50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | | 50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 ||| | | |50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 ||| | | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 ||| | | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 ||| |2*re|atan|- -- + ------------------------ + -----------|| + 2*I*im|atan|- -- + ------------------------ + -----------|||*|- 2*re|atan|-- + ------------------------ - -----------|| - 2*I*im|atan|-- + ------------------------ - -----------|||*|- 2*re|atan|-- - ------------------------ + -----------|| - 2*I*im|atan|-- - ------------------------ + -----------|||*|- 2*re|atan|-- + ------------------------ + -----------|| - 2*I*im|atan|-- + ------------------------ + -----------||| \ \ \ 77 77 77 // \ \ 77 77 77 /// \ \ \77 77 77 // \ \77 77 77 /// \ \ \77 77 77 // \ \77 77 77 /// \ \ \77 77 77 // \ \77 77 77 ///
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{50}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{50}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{3 \sqrt{381} i}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{3 \sqrt{381} i}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} + \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} + \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}\right)$$
=
/ / / __________________ \\ / / __________________ \\\ / / / __________________ \\ / / __________________ \\\ / / / __________________ \\ / / __________________ \\\ / / / __________________ \\ / / __________________ \\\
| | | / _____ _____|| | | / _____ _____||| | | | / _____ _____|| | | / _____ _____||| | | | / _____ _____|| | | / _____ _____||| | | | / _____ _____|| | | / _____ _____|||
| | | 50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | | 50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 ||| | | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 ||| | | |50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 - 3*I*\/ 381 3*I*\/ 381 ||| | | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 || | |50 10*\/ 50 + 3*I*\/ 381 3*I*\/ 381 |||
-16*|I*im|atan|- -- + ------------------------ + -----------|| + re|atan|- -- + ------------------------ + -----------|||*|I*im|atan|-- - ------------------------ + -----------|| + re|atan|-- - ------------------------ + -----------|||*|I*im|atan|-- + ------------------------ - -----------|| + re|atan|-- + ------------------------ - -----------|||*|I*im|atan|-- + ------------------------ + -----------|| + re|atan|-- + ------------------------ + -----------|||
\ \ \ 77 77 77 // \ \ 77 77 77 /// \ \ \77 77 77 // \ \77 77 77 /// \ \ \77 77 77 // \ \77 77 77 /// \ \ \77 77 77 // \ \77 77 77 ///
$$- 16 \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{50}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{50}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{3 \sqrt{381} i}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{3 \sqrt{381} i}{77} + \frac{10 \sqrt{50 - 3 \sqrt{381} i}}{77} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} - \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{50}{77} + \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{50}{77} + \frac{10 \sqrt{50 + 3 \sqrt{381} i}}{77} + \frac{3 \sqrt{381} i}{77} \right)}\right)}\right)$$
-16*(i*im(atan(-50/77 + 10*sqrt(50 - 3*i*sqrt(381))/77 + 3*i*sqrt(381)/77)) + re(atan(-50/77 + 10*sqrt(50 - 3*i*sqrt(381))/77 + 3*i*sqrt(381)/77)))*(i*im(atan(50/77 - 10*sqrt(50 + 3*i*sqrt(381))/77 + 3*i*sqrt(381)/77)) + re(atan(50/77 - 10*sqrt(50 + 3*i*sqrt(381))/77 + 3*i*sqrt(381)/77)))*(i*im(atan(50/77 + 10*sqrt(50 - 3*i*sqrt(381))/77 - 3*i*sqrt(381)/77)) + re(atan(50/77 + 10*sqrt(50 - 3*i*sqrt(381))/77 - 3*i*sqrt(381)/77)))*(i*im(atan(50/77 + 10*sqrt(50 + 3*i*sqrt(381))/77 + 3*i*sqrt(381)/77)) + re(atan(50/77 + 10*sqrt(50 + 3*i*sqrt(381))/77 + 3*i*sqrt(381)/77)))
Respuesta numérica
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x1 = 0.785398163397448 + 0.498687054056429*i
x2 = -2.35619449019234 + 0.498687054056429*i
x3 = 0.785398163397448 - 0.498687054056429*i
x4 = -2.35619449019234 - 0.498687054056429*i
x4 = -2.35619449019234 - 0.498687054056429*i