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- La ecuación:
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Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
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Ecuación x^2+4=5x
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Ecuación x(x^2+2x+1)=6(x+1)
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Ecuación 4x+1=-3x+15
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -17*x-15*y=-17
- -9*x+11*y=9
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Expresiones idénticas
- (cos(t)+ dos)* tres *k- dos *sin(t)= cero
- ( coseno de (t) más 2) multiplicar por 3 multiplicar por k menos 2 multiplicar por seno de (t) es igual a 0
- ( coseno de (t) más dos) multiplicar por tres multiplicar por k menos dos multiplicar por seno de (t) es igual a cero
- (cos(t)+2)3k-2sin(t)=0
- cost+23k-2sint=0
- (cos(t)+2)*3*k-2*sin(t)=O
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Expresiones semejantes
- (cos(t)-2)*3*k-2*sin(t)=0
- (cos(t)+2)*3*k+2*sin(t)=0
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Expresiones con funciones
- Coseno cos
- cos(x)=-8
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- Seno sin
- sin(x)=pi
- sin(4*x)=0
- sin(x)^2=1
- sin(x)=(1/2)
- sin(x)=0,5
(cos(t)+2)*3*k-2*sin(t)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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(cos(t) + 2)*3*k - 2*sin(t) = 0
$$k 3 \left(\cos{\left(t \right)} + 2\right) - 2 \sin{\left(t \right)} = 0$$
Gráfica
Suma y producto de raíces
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suma
/ / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\
| | / 2 || | | / 2 || | | / 2 || | | / 2 ||
| |-2 + \/ 4 - 27*k || | |-2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k ||
- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|| + 2*re|atan|------------------|| + 2*I*im|atan|------------------||
\ \ 3*k // \ \ 3*k // \ \ 3*k // \ \ 3*k //
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)}\right)$$
=
/ / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\
| | / 2 || | | / 2 || | | / 2 || | | / 2 ||
| |-2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k || | |-2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k ||
- 2*re|atan|-------------------|| + 2*re|atan|------------------|| - 2*I*im|atan|-------------------|| + 2*I*im|atan|------------------||
\ \ 3*k // \ \ 3*k // \ \ 3*k // \ \ 3*k //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)}$$
producto
/ / / ___________\\ / / ___________\\\ / / / ___________\\ / / ___________\\\ | | | / 2 || | | / 2 ||| | | | / 2 || | | / 2 ||| | | |-2 + \/ 4 - 27*k || | |-2 + \/ 4 - 27*k ||| | | |2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k ||| |- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|||*|2*re|atan|------------------|| + 2*I*im|atan|------------------||| \ \ \ 3*k // \ \ 3*k /// \ \ \ 3*k // \ \ 3*k ///
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)}\right)$$
=
/ / / ___________\\ / / ___________\\\ / / / ___________\\ / / ___________\\\ | | | / 2 || | | / 2 ||| | | | / 2 || | | / 2 ||| | | |-2 + \/ 4 - 27*k || | |-2 + \/ 4 - 27*k ||| | | |2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k ||| -4*|I*im|atan|-------------------|| + re|atan|-------------------|||*|I*im|atan|------------------|| + re|atan|------------------||| \ \ \ 3*k // \ \ 3*k /// \ \ \ 3*k // \ \ 3*k ///
$$- 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)}\right)$$
-4*(i*im(atan((-2 + sqrt(4 - 27*k^2))/(3*k))) + re(atan((-2 + sqrt(4 - 27*k^2))/(3*k))))*(i*im(atan((2 + sqrt(4 - 27*k^2))/(3*k))) + re(atan((2 + sqrt(4 - 27*k^2))/(3*k))))
Respuesta rápida
[src]
/ / ___________\\ / / ___________\\
| | / 2 || | | / 2 ||
| |-2 + \/ 4 - 27*k || | |-2 + \/ 4 - 27*k ||
t1 = - 2*re|atan|-------------------|| - 2*I*im|atan|-------------------||
\ \ 3*k // \ \ 3*k //
$$t_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)}$$
/ / ___________\\ / / ___________\\
| | / 2 || | | / 2 ||
| |2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k ||
t2 = 2*re|atan|------------------|| + 2*I*im|atan|------------------||
\ \ 3*k // \ \ 3*k //
$$t_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)}$$
t2 = 2*re(atan((sqrt(4 - 27*k^2) + 2)/(3*k))) + 2*i*im(atan((sqrt(4 - 27*k^2) + 2)/(3*k)))