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- La ecuación:
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Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
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Ecuación x^2-14*x+33=0
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Ecuación 5-x^2=0
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 14*x-10*y=-4
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Expresiones idénticas
- dos *p^ dos -(p^ dos *sin(x)^(dos)+ cuatro)= cero
- 2 multiplicar por p al cuadrado menos (p al cuadrado multiplicar por seno de (x) en el grado (2) más 4) es igual a 0
- dos multiplicar por p en el grado dos menos (p en el grado dos multiplicar por seno de (x) en el grado (dos) más cuatro) es igual a cero
- 2*p2-(p2*sin(x)(2)+4)=0
- 2*p2-p2*sinx2+4=0
- 2*p²-(p²*sin(x)^(2)+4)=0
- 2*p en el grado 2-(p en el grado 2*sin(x) en el grado (2)+4)=0
- 2p^2-(p^2sin(x)^(2)+4)=0
- 2p2-(p2sin(x)(2)+4)=0
- 2p2-p2sinx2+4=0
- 2p^2-p^2sinx^2+4=0
- 2*p^2-(p^2*sin(x)^(2)+4)=O
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Expresiones semejantes
- 2*p^2+(p^2*sin(x)^(2)+4)=0
- 2*p^2-(p^2*sin(x)^(2)-4)=0
- 2*p^2-(p^2*sinx^(2)+4)=0
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Expresiones con funciones
- Seno sin
- sin(x)=√2
- sin(pi*x/6)=-1
- sin(x)=4/5
- sin(x)+cos(x)=0
- sin(x)=1
2*p^2-(p^2*sin(x)^(2)+4)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 2 2*p + - p *sin (x) - 4 = 0
$$2 p^{2} + \left(- p^{2} \sin^{2}{\left(x \right)} - 4\right) = 0$$
Solución detallada
Tenemos la ecuación
$$2 p^{2} + \left(- p^{2} \sin^{2}{\left(x \right)} - 4\right) = 0$$
cambiamos
$$p^{2} \cos^{2}{\left(x \right)} + p^{2} - 4 = 0$$
$$2 p^{2} + \left(- p^{2} \sin^{2}{\left(x \right)} - 4\right) = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = - p^{2}$$
$$b = 0$$
$$c = 2 p^{2} - 4$$
, entonces
La ecuación tiene dos raíces.
o
$$w_{1} = - \frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}}$$
$$w_{2} = \frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}}$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)}$$
$$x_{1} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)} + \pi$$
$$x_{3} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)} + \pi$$
$$2 p^{2} + \left(- p^{2} \sin^{2}{\left(x \right)} - 4\right) = 0$$
cambiamos
$$p^{2} \cos^{2}{\left(x \right)} + p^{2} - 4 = 0$$
$$2 p^{2} + \left(- p^{2} \sin^{2}{\left(x \right)} - 4\right) = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Es la ecuación de la forma
a*w^2 + b*w + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = - p^{2}$$
$$b = 0$$
$$c = 2 p^{2} - 4$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-p^2) * (-4 + 2*p^2) = 4*p^2*(-4 + 2*p^2)
La ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
o
$$w_{1} = - \frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}}$$
$$w_{2} = \frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}}$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)}$$
$$x_{1} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)} + \pi$$
$$x_{3} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{p^{2} \left(2 p^{2} - 4\right)}}{p^{2}} \right)} + \pi$$
Gráfica
Suma y producto de raíces
[src]
suma
/ / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\
| | / 2 || | | / 2 || | | / 2 || | | / 2 || | | / 2 || | | / 2 || | | / 2 || | | / 2 ||
| |\/ -4 + 2*p || | |\/ -4 + 2*p || | |\/ -4 + 2*p || | |\/ -4 + 2*p || | |\/ -4 + 2*p || | |\/ -4 + 2*p || | |\/ -4 + 2*p || | |\/ -4 + 2*p ||
pi - re|asin|--------------|| - I*im|asin|--------------|| + pi + I*im|asin|--------------|| + re|asin|--------------|| + - re|asin|--------------|| - I*im|asin|--------------|| + I*im|asin|--------------|| + re|asin|--------------||
\ \ p // \ \ p // \ \ p // \ \ p // \ \ p // \ \ p // \ \ p // \ \ p //
$$\left(\left(\left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + \pi\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + \pi\right)\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)}\right)$$
=
2*pi
$$2 \pi$$
producto
/ / / ___________\\ / / ___________\\\ / / / ___________\\ / / ___________\\\ / / / ___________\\ / / ___________\\\ / / / ___________\\ / / ___________\\\ | | | / 2 || | | / 2 ||| | | | / 2 || | | / 2 ||| | | | / 2 || | | / 2 ||| | | | / 2 || | | / 2 ||| | | |\/ -4 + 2*p || | |\/ -4 + 2*p ||| | | |\/ -4 + 2*p || | |\/ -4 + 2*p ||| | | |\/ -4 + 2*p || | |\/ -4 + 2*p ||| | | |\/ -4 + 2*p || | |\/ -4 + 2*p ||| |pi - re|asin|--------------|| - I*im|asin|--------------|||*|pi + I*im|asin|--------------|| + re|asin|--------------|||*|- re|asin|--------------|| - I*im|asin|--------------|||*|I*im|asin|--------------|| + re|asin|--------------||| \ \ \ p // \ \ p /// \ \ \ p // \ \ p /// \ \ \ p // \ \ p /// \ \ \ p // \ \ p ///
$$\left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + \pi\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + \pi\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)}\right)$$
=
2 / / / _________\\ / / _________\\\ / / / _________\\ / / _________\\\ / / / _________\\ / / _________\\\ | | | ___ / 2 || | | ___ / 2 ||| | | | ___ / 2 || | | ___ / 2 ||| | | | ___ / 2 || | | ___ / 2 ||| | | |\/ 2 *\/ -2 + p || | |\/ 2 *\/ -2 + p ||| | | |\/ 2 *\/ -2 + p || | |\/ 2 *\/ -2 + p ||| | | |\/ 2 *\/ -2 + p || | |\/ 2 *\/ -2 + p ||| |I*im|asin|------------------|| + re|asin|------------------||| *|pi + I*im|asin|------------------|| + re|asin|------------------|||*|-pi + I*im|asin|------------------|| + re|asin|------------------||| \ \ \ p // \ \ p /// \ \ \ p // \ \ p /// \ \ \ p // \ \ p ///
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{p^{2} - 2}}{p} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{p^{2} - 2}}{p} \right)}\right)}\right)^{2} \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{p^{2} - 2}}{p} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{p^{2} - 2}}{p} \right)}\right)} - \pi\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{p^{2} - 2}}{p} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{p^{2} - 2}}{p} \right)}\right)} + \pi\right)$$
(i*im(asin(sqrt(2)*sqrt(-2 + p^2)/p)) + re(asin(sqrt(2)*sqrt(-2 + p^2)/p)))^2*(pi + i*im(asin(sqrt(2)*sqrt(-2 + p^2)/p)) + re(asin(sqrt(2)*sqrt(-2 + p^2)/p)))*(-pi + i*im(asin(sqrt(2)*sqrt(-2 + p^2)/p)) + re(asin(sqrt(2)*sqrt(-2 + p^2)/p)))
Respuesta rápida
[src]
/ / ___________\\ / / ___________\\
| | / 2 || | | / 2 ||
| |\/ -4 + 2*p || | |\/ -4 + 2*p ||
x1 = pi - re|asin|--------------|| - I*im|asin|--------------||
\ \ p // \ \ p //
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + \pi$$
/ / ___________\\ / / ___________\\
| | / 2 || | | / 2 ||
| |\/ -4 + 2*p || | |\/ -4 + 2*p ||
x2 = pi + I*im|asin|--------------|| + re|asin|--------------||
\ \ p // \ \ p //
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + \pi$$
/ / ___________\\ / / ___________\\
| | / 2 || | | / 2 ||
| |\/ -4 + 2*p || | |\/ -4 + 2*p ||
x3 = - re|asin|--------------|| - I*im|asin|--------------||
\ \ p // \ \ p //
$$x_{3} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)}$$
/ / ___________\\ / / ___________\\
| | / 2 || | | / 2 ||
| |\/ -4 + 2*p || | |\/ -4 + 2*p ||
x4 = I*im|asin|--------------|| + re|asin|--------------||
\ \ p // \ \ p //
$$x_{4} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\sqrt{2 p^{2} - 4}}{p} \right)}\right)}$$
x4 = re(asin(sqrt(2*p^2 - 4)/p)) + i*im(asin(sqrt(2*p^2 - 4)/p))