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- La ecuación:
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Ecuación -x+7=0
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Ecuación x+(x/4)=-5
- Ecuación z^4-81=0
-
Ecuación z^3=8
- Expresar {x} en función de y en la ecuación:
- -18*x-8*y=-18
- -13*x+12*y=-19
- -1*x+11*y=-9
- 16*x-11*y=13
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Expresiones idénticas
- f=cos^4t
- f es igual a coseno de en el grado 4t
- f=cos4t
- f=cos⁴t
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Expresiones con funciones
- Coseno cos
- cos(3*x)-cos(7x)=0
- cos(x)+cos(2*x)+cos(3*x)=3
- cos(x)=cos(4)
- cos^2(x)=0.1*e^x
- cos(x)*sin(x)=-1/2
f=cos^4t la ecuación
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Solución
Gráfica
Suma y producto de raíces
[src]
suma
pi / /4 ___\\ / /4 ___\\ 3*pi / /4 ___\\ / /4 ___\\ pi / /4 ___\\ / /4 ___\\ / /4 ___\\ 3*pi / /4 ___\\ / / 4 ___\\ / / 4 ___\\ / /4 ___\\ / /4 ___\\ / / 4 ___\\ / / 4 ___\\ / /4 ___\\ / /4 ___\\ -- - I*re\asinh\\/ f // + im\asinh\\/ f // + ---- - I*re\asinh\\/ f // + im\asinh\\/ f // + -- - im\asinh\\/ f // + I*re\asinh\\/ f // + - im\asinh\\/ f // + ---- + I*re\asinh\\/ f // + - re\acos\-\/ f // + 2*pi - I*im\acos\-\/ f // + - re\acos\\/ f // + 2*pi - I*im\acos\\/ f // + I*im\acos\-\/ f // + re\acos\-\/ f // + I*im\acos\\/ f // + re\acos\\/ f // 2 2 2 2
$$\left(\left(\left(\left(\left(\left(\left(- i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{\pi}{2}\right) + \left(- i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{3 \pi}{2}\right)\right) + \left(i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} - \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{\pi}{2}\right)\right) + \left(i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} - \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{3 \pi}{2}\right)\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} + 2 \pi\right)\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} + 2 \pi\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)}\right)$$
=
8*pi
$$8 \pi$$
producto
/pi / /4 ___\\ / /4 ___\\\ /3*pi / /4 ___\\ / /4 ___\\\ /pi / /4 ___\\ / /4 ___\\\ / / /4 ___\\ 3*pi / /4 ___\\\ / / / 4 ___\\ / / 4 ___\\\ / / /4 ___\\ / /4 ___\\\ / / / 4 ___\\ / / 4 ___\\\ / / /4 ___\\ / /4 ___\\\ |-- - I*re\asinh\\/ f // + im\asinh\\/ f //|*|---- - I*re\asinh\\/ f // + im\asinh\\/ f //|*|-- - im\asinh\\/ f // + I*re\asinh\\/ f //|*|- im\asinh\\/ f // + ---- + I*re\asinh\\/ f //|*\- re\acos\-\/ f // + 2*pi - I*im\acos\-\/ f ///*\- re\acos\\/ f // + 2*pi - I*im\acos\\/ f ///*\I*im\acos\-\/ f // + re\acos\-\/ f ///*\I*im\acos\\/ f // + re\acos\\/ f /// \2 / \ 2 / \2 / \ 2 /
$$\left(- i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{\pi}{2}\right) \left(- i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{3 \pi}{2}\right) \left(i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} - \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{\pi}{2}\right) \left(i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} - \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{3 \pi}{2}\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} + 2 \pi\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} + 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)}\right)$$
=
/ / /4 ___\\ / /4 ___\\\ / / / 4 ___\\ / / 4 ___\\\ / / /4 ___\\ / /4 ___\\\ / / /4 ___\\ / /4 ___\\\ / / /4 ___\\ / /4 ___\\\ / / / 4 ___\\ / / 4 ___\\\ / / /4 ___\\ / /4 ___\\\ / / /4 ___\\ / /4 ___\\\
\I*im\acos\\/ f // + re\acos\\/ f ///*\I*im\acos\-\/ f // + re\acos\-\/ f ///*\pi - 2*im\asinh\\/ f // + 2*I*re\asinh\\/ f ///*\pi + 2*im\asinh\\/ f // - 2*I*re\asinh\\/ f ///*\-2*pi + I*im\acos\\/ f // + re\acos\\/ f ///*\-2*pi + I*im\acos\-\/ f // + re\acos\-\/ f ///*\- 2*im\asinh\\/ f // + 3*pi + 2*I*re\asinh\\/ f ///*\2*im\asinh\\/ f // + 3*pi - 2*I*re\asinh\\/ f ///
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16
$$\frac{\left(\operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)}\right) \left(- 2 i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + 2 \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \pi\right) \left(- 2 i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + 2 \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + 3 \pi\right) \left(2 i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} - 2 \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \pi\right) \left(2 i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} - 2 \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + 3 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} - 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} - 2 \pi\right)}{16}$$
(i*im(acos(f^(1/4))) + re(acos(f^(1/4))))*(i*im(acos(-f^(1/4))) + re(acos(-f^(1/4))))*(pi - 2*im(asinh(f^(1/4))) + 2*i*re(asinh(f^(1/4))))*(pi + 2*im(asinh(f^(1/4))) - 2*i*re(asinh(f^(1/4))))*(-2*pi + i*im(acos(f^(1/4))) + re(acos(f^(1/4))))*(-2*pi + i*im(acos(-f^(1/4))) + re(acos(-f^(1/4))))*(-2*im(asinh(f^(1/4))) + 3*pi + 2*i*re(asinh(f^(1/4))))*(2*im(asinh(f^(1/4))) + 3*pi - 2*i*re(asinh(f^(1/4))))/16
Respuesta rápida
[src]
pi / /4 ___\\ / /4 ___\\
t1 = -- - I*re\asinh\\/ f // + im\asinh\\/ f //
2
$$t_{1} = - i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{\pi}{2}$$
3*pi / /4 ___\\ / /4 ___\\
t2 = ---- - I*re\asinh\\/ f // + im\asinh\\/ f //
2
$$t_{2} = - i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{3 \pi}{2}$$
pi / /4 ___\\ / /4 ___\\
t3 = -- - im\asinh\\/ f // + I*re\asinh\\/ f //
2
$$t_{3} = i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} - \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{\pi}{2}$$
/ /4 ___\\ 3*pi / /4 ___\\
t4 = - im\asinh\\/ f // + ---- + I*re\asinh\\/ f //
2
$$t_{4} = i \operatorname{re}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} - \operatorname{im}{\left(\operatorname{asinh}{\left(\sqrt[4]{f} \right)}\right)} + \frac{3 \pi}{2}$$
/ / 4 ___\\ / / 4 ___\\ t5 = - re\acos\-\/ f // + 2*pi - I*im\acos\-\/ f //
$$t_{5} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} + 2 \pi$$
/ /4 ___\\ / /4 ___\\ t6 = - re\acos\\/ f // + 2*pi - I*im\acos\\/ f //
$$t_{6} = - \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} + 2 \pi$$
/ / 4 ___\\ / / 4 ___\\ t7 = I*im\acos\-\/ f // + re\acos\-\/ f //
$$t_{7} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[4]{f} \right)}\right)}$$
/ /4 ___\\ / /4 ___\\ t8 = I*im\acos\\/ f // + re\acos\\/ f //
$$t_{8} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[4]{f} \right)}\right)}$$
t8 = re(acos(f^(1/4))) + i*im(acos(f^(1/4)))