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- La ecuación:
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Ecuación 8*x=2
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Ecuación 3^x=81
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Ecuación 5x+15=x-1
-
Ecuación x^2=12
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- 9*x+17*y=13
- -17*x+2*y=9
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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
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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
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2 / 2 \ 8*cos (x)*\2*cos (x) - 1/ = 9
$$\left(2 \cos^{2}{\left(x \right)} - 1\right) 8 \cos^{2}{\left(x \right)} = 9$$
Respuesta rápida
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/ ______________\
| / ____ |
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
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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 ///
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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
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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