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- La ecuación:
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Ecuación 8*x-3*(2*x+1)=2*x+4
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Ecuación x^3=27
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Ecuación 1+sin(x)=0
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Ecuación 2*x^2+6*x+9=
- Expresar {x} en función de y en la ecuación:
- 20*x+6*y=8
- -11*x-15*y=14
- -11*x+10*y=-9
- 6*x-2*y=20
- Derivada de:
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sqrt(3)/2
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Expresiones idénticas
- cospi(4x- siete)/ seis =sqrt(tres)/ dos
- coseno de número pi (4x menos 7) dividir por 6 es igual a raíz cuadrada de (3) dividir por 2
- coseno de número pi (4x menos siete) dividir por seis es igual a raíz cuadrada de (tres) dividir por dos
- cospi(4x-7)/6=√(3)/2
- cospi4x-7/6=sqrt3/2
- cospi(4x-7) dividir por 6=sqrt(3) dividir por 2
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Expresiones semejantes
- 100*sqrt(x^2/25+1)/((x^2*sqrt((3/200)^2*x^2+1)))=1
- cospi(4x+7)/6=sqrt(3)/2
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Expresiones con funciones
- cospi
- cospi(4*x-6)/3=12
- cospix=-2
- cospix=6
- cospi(2x+36)/4=-sqrt(2)/2
- Raíz cuadrada sqrt
- sqrt(3)/2*cos(x)-1/2*sin(x)=1
- sqrt(x+2)=x
- sqrt(x)=0
- sqrt(x+1)-sqrt(4-x)+3=2*sqrt(4+3x-x^2)
- sqrt(x^2-36)+sqrt(x^2-64)=28/(x-8)
cospi(4x-7)/6=sqrt(3)/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___
cos(p)*I*(4*x - 7) \/ 3
------------------ = -----
6 2
$$\frac{i \cos{\left(p \right)} \left(4 x - 7\right)}{6} = \frac{\sqrt{3}}{2}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \cos{\left(p \right)} \left(4 x - 7\right)}{6} = \frac{\sqrt{3}}{2}$$
cambiamos
$$\frac{i \left(4 x - 7\right) \cos{\left(p \right)}}{6} - 1 - \frac{\sqrt{3}}{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(4 x - 7\right)}{6} - 1 - \frac{\sqrt{3}}{2} = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(4 x - 7\right)}{6} - \frac{\sqrt{3}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (-sqrt(3)/2 + i*w*(-7 + 4*x)/6)/w
Obtenemos la respuesta: w = -3*i*(2 + sqrt(3))/(-7 + 4*x)
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \cos{\left(p \right)} \left(4 x - 7\right)}{6} = \frac{\sqrt{3}}{2}$$
cambiamos
$$\frac{i \left(4 x - 7\right) \cos{\left(p \right)}}{6} - 1 - \frac{\sqrt{3}}{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(4 x - 7\right)}{6} - 1 - \frac{\sqrt{3}}{2} = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - sqrt3/2 + i*w4*x/6+7/6 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 - sqrt(3)/2 + i*w*(-7 + 4*x)/6 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(4 x - 7\right)}{6} - \frac{\sqrt{3}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (-sqrt(3)/2 + i*w*(-7 + 4*x)/6)/w
w = 1 / ((-sqrt(3)/2 + i*w*(-7 + 4*x)/6)/w)
Obtenemos la respuesta: w = -3*i*(2 + sqrt(3))/(-7 + 4*x)
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida
[src]
___ ___
7 3*\/ 3 *sin(re(p))*sinh(im(p)) 3*I*\/ 3 *cos(re(p))*cosh(im(p))
x1 = - + ------------------------------------------------------- - -------------------------------------------------------
4 / 2 2 2 2 \ / 2 2 2 2 \
4*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/ 4*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$x_{1} = \frac{7}{4} + \frac{3 \sqrt{3} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \sqrt{3} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
x1 = 7/4 + 3*sqrt(3)*sin(re(p))*sinh(im(p))/(4*(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2)) - 3*sqrt(3)*i*cos(re(p))*cosh(im(p))/(4*(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2))
Suma y producto de raíces
[src]
suma
___ ___
7 3*\/ 3 *sin(re(p))*sinh(im(p)) 3*I*\/ 3 *cos(re(p))*cosh(im(p))
- + ------------------------------------------------------- - -------------------------------------------------------
4 / 2 2 2 2 \ / 2 2 2 2 \
4*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/ 4*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$\frac{7}{4} + \frac{3 \sqrt{3} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \sqrt{3} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
___ ___
7 3*\/ 3 *sin(re(p))*sinh(im(p)) 3*I*\/ 3 *cos(re(p))*cosh(im(p))
- + ------------------------------------------------------- - -------------------------------------------------------
4 / 2 2 2 2 \ / 2 2 2 2 \
4*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/ 4*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$\frac{7}{4} + \frac{3 \sqrt{3} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \sqrt{3} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
producto
___ ___
7 3*\/ 3 *sin(re(p))*sinh(im(p)) 3*I*\/ 3 *cos(re(p))*cosh(im(p))
- + ------------------------------------------------------- - -------------------------------------------------------
4 / 2 2 2 2 \ / 2 2 2 2 \
4*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/ 4*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$\frac{7}{4} + \frac{3 \sqrt{3} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \sqrt{3} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
/ ___ \
I*\3*\/ 3 + 7*sin(re(p))*sinh(im(p))/ - 7*cos(re(p))*cosh(im(p))
-----------------------------------------------------------------
4*(-cos(re(p))*cosh(im(p)) + I*sin(re(p))*sinh(im(p)))
$$\frac{i \left(7 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + 3 \sqrt{3}\right) - 7 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
(i*(3*sqrt(3) + 7*sin(re(p))*sinh(im(p))) - 7*cos(re(p))*cosh(im(p)))/(4*(-cos(re(p))*cosh(im(p)) + i*sin(re(p))*sinh(im(p))))