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- La ecuación:
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Ecuación x^4+2*x^2-8=0
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Ecuación x*(x^2+8*x+16)=5*(x+4)
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Ecuación ((57.6/(150-x))^0.15)*((150+x)+10)/171.712=1
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Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
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Expresiones idénticas
- arctg(c)+arctg(x)=-arctg(y)
- arctg(c) más arctg(x) es igual a menos arctg(y)
- arctgc+arctgx=-arctgy
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Expresiones semejantes
- arctg(c)-arctg(x)=-arctg(y)
- arctg(c)+arctg(x)=+arctg(y)
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Expresiones con funciones
- arctg
- arctg(x/y)
- arctg(t)
- Arctg3x/x
- arctgx-ln((2*y+3)^(1/2))=0
- arctg(xy)
- arctg
- arctg(x/y)
- arctg(t)
- Arctg3x/x
- arctgx-ln((2*y+3)^(1/2))=0
- arctg(xy)
- arctg
- arctg(x/y)
- arctg(t)
- Arctg3x/x
- arctgx-ln((2*y+3)^(1/2))=0
- arctg(xy)
arctg(c)+arctg(x)=-arctg(y) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
atan(c) + atan(x) = -atan(y)
$$\operatorname{atan}{\left(c \right)} + \operatorname{atan}{\left(x \right)} = - \operatorname{atan}{\left(y \right)}$$
Gráfica
Suma y producto de raíces
[src]
suma
/(-1 + re(c*y))*(im(c) + im(y)) (re(c) + re(y))*im(c*y) \ (-1 + re(c*y))*(re(c) + re(y)) (im(c) + im(y))*im(c*y) I*|------------------------------ - --------------------------| + ------------------------------ + -------------------------- | 2 2 2 2 | 2 2 2 2 \ (-1 + re(c*y)) + im (c*y) (-1 + re(c*y)) + im (c*y)/ (-1 + re(c*y)) + im (c*y) (-1 + re(c*y)) + im (c*y)
$$i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(c y\right)} - 1\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c y\right)} - 1\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}}$$
=
/(-1 + re(c*y))*(im(c) + im(y)) (re(c) + re(y))*im(c*y) \ (-1 + re(c*y))*(re(c) + re(y)) (im(c) + im(y))*im(c*y) I*|------------------------------ - --------------------------| + ------------------------------ + -------------------------- | 2 2 2 2 | 2 2 2 2 \ (-1 + re(c*y)) + im (c*y) (-1 + re(c*y)) + im (c*y)/ (-1 + re(c*y)) + im (c*y) (-1 + re(c*y)) + im (c*y)
$$i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(c y\right)} - 1\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c y\right)} - 1\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}}$$
producto
/(-1 + re(c*y))*(im(c) + im(y)) (re(c) + re(y))*im(c*y) \ (-1 + re(c*y))*(re(c) + re(y)) (im(c) + im(y))*im(c*y) I*|------------------------------ - --------------------------| + ------------------------------ + -------------------------- | 2 2 2 2 | 2 2 2 2 \ (-1 + re(c*y)) + im (c*y) (-1 + re(c*y)) + im (c*y)/ (-1 + re(c*y)) + im (c*y) (-1 + re(c*y)) + im (c*y)
$$i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(c y\right)} - 1\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c y\right)} - 1\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}}$$
=
I*((-1 + re(c*y))*(im(c) + im(y)) - (re(c) + re(y))*im(c*y)) + (-1 + re(c*y))*(re(c) + re(y)) + (im(c) + im(y))*im(c*y)
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2 2
(-1 + re(c*y)) + im (c*y)
$$\frac{i \left(- \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)} + \left(\operatorname{re}{\left(c y\right)} - 1\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right)\right) + \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c y\right)} - 1\right) + \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}}$$
(i*((-1 + re(c*y))*(im(c) + im(y)) - (re(c) + re(y))*im(c*y)) + (-1 + re(c*y))*(re(c) + re(y)) + (im(c) + im(y))*im(c*y))/((-1 + re(c*y))^2 + im(c*y)^2)