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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(x^2+2x+1)=6(x+1)
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Ecuación 4x+1=-3x+15
- Ecuación (3x−36)⋅(x+8)=0
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
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Expresiones idénticas
- (uno + dos *(cos(x)+sin(x))^ dos /(-cos(x)+sin(x))^ dos)/(-cos(x)+sin(x))= cero
- (1 más 2 multiplicar por ( coseno de (x) más seno de (x)) al cuadrado dividir por ( menos coseno de (x) más seno de (x)) al cuadrado ) dividir por ( menos coseno de (x) más seno de (x)) es igual a 0
- (uno más dos multiplicar por ( coseno de (x) más seno de (x)) en el grado dos dividir por ( menos coseno de (x) más seno de (x)) en el grado dos) dividir por ( menos coseno de (x) más seno de (x)) es igual a cero
- (1+2*(cos(x)+sin(x))2/(-cos(x)+sin(x))2)/(-cos(x)+sin(x))=0
- 1+2*cosx+sinx2/-cosx+sinx2/-cosx+sinx=0
- (1+2*(cos(x)+sin(x))²/(-cos(x)+sin(x))²)/(-cos(x)+sin(x))=0
- (1+2*(cos(x)+sin(x)) en el grado 2/(-cos(x)+sin(x)) en el grado 2)/(-cos(x)+sin(x))=0
- (1+2(cos(x)+sin(x))^2/(-cos(x)+sin(x))^2)/(-cos(x)+sin(x))=0
- (1+2(cos(x)+sin(x))2/(-cos(x)+sin(x))2)/(-cos(x)+sin(x))=0
- 1+2cosx+sinx2/-cosx+sinx2/-cosx+sinx=0
- 1+2cosx+sinx^2/-cosx+sinx^2/-cosx+sinx=0
- (1+2*(cos(x)+sin(x))^2/(-cos(x)+sin(x))^2)/(-cos(x)+sin(x))=O
- (1+2*(cos(x)+sin(x))^2 dividir por (-cos(x)+sin(x))^2) dividir por (-cos(x)+sin(x))=0
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Expresiones semejantes
- (1-2*(cos(x)+sin(x))^2/(-cos(x)+sin(x))^2)/(-cos(x)+sin(x))=0
- (1+2*(cos(x)+sin(x))^2/(-cos(x)+sin(x))^2)/(-cos(x)-sin(x))=0
- (1+2*(cos(x)+sin(x))^2/(-cos(x)+sin(x))^2)/(cos(x)+sin(x))=0
- (1+2*(cos(x)+sin(x))^2/(-cos(x)-sin(x))^2)/(-cos(x)+sin(x))=0
- (1+2*(cos(x)-sin(x))^2/(-cos(x)+sin(x))^2)/(-cos(x)+sin(x))=0
- (1+2*(cos(x)+sin(x))^2/(cos(x)+sin(x))^2)/(-cos(x)+sin(x))=0
- (1+2*(cosx+sinx)^2/(-cosx+sinx)^2)/(-cosx+sinx)=0
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Expresiones con funciones
- Coseno cos
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- cos(x)=1/2
- Seno sin
- sin(x)=pi
- sin(4*x)=0
- sin(x)^2=1
- sin(x)=(1/2)
- sin(x)+sin(2*x)+sin(3*x)=0
- Coseno cos
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- cos(x)=1/2
- Seno sin
- sin(x)=pi
- sin(4*x)=0
- sin(x)^2=1
- sin(x)=(1/2)
- sin(x)+sin(2*x)+sin(3*x)=0
- Coseno cos
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- cos(x)=1/2
- Seno sin
- sin(x)=pi
- sin(4*x)=0
- sin(x)^2=1
- sin(x)=(1/2)
- sin(x)+sin(2*x)+sin(3*x)=0
(1+2*(cos(x)+sin(x))^2/(-cos(x)+sin(x))^2)/(-cos(x)+sin(x))=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2
2*(cos(x) + sin(x))
1 + --------------------
2
(-cos(x) + sin(x))
------------------------ = 0
-cos(x) + sin(x)
$$\frac{1 + \frac{2 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}}{\sin{\left(x \right)} - \cos{\left(x \right)}} = 0$$
Respuesta rápida
[src]
/ / ___\\ / / ___\\
| |1 I*\/ 2 || | |1 I*\/ 2 ||
x1 = - 2*re|atan|- - -------|| - 2*I*im|atan|- - -------||
\ \3 3 // \ \3 3 //
$$x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)}$$
/ / ___\\ / / ___\\
| |1 I*\/ 2 || | |1 I*\/ 2 ||
x2 = - 2*re|atan|- + -------|| - 2*I*im|atan|- + -------||
\ \3 3 // \ \3 3 //
$$x_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)}$$
/ / ___\\ / / ___\\ x3 = 2*re\atan\1 - I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 //
$$x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}$$
/ / ___\\ / / ___\\ x4 = 2*re\atan\1 + I*\/ 2 // + 2*I*im\atan\1 + I*\/ 2 //
$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}$$
x4 = 2*re(atan(1 + sqrt(2)*i)) + 2*i*im(atan(1 + sqrt(2)*i))
Suma y producto de raíces
[src]
suma
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| |1 I*\/ 2 || | |1 I*\/ 2 || | |1 I*\/ 2 || | |1 I*\/ 2 || / / ___\\ / / ___\\ / / ___\\ / / ___\\
- 2*re|atan|- - -------|| - 2*I*im|atan|- - -------|| + - 2*re|atan|- + -------|| - 2*I*im|atan|- + -------|| + 2*re\atan\1 - I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 // + 2*re\atan\1 + I*\/ 2 // + 2*I*im\atan\1 + I*\/ 2 //
\ \3 3 // \ \3 3 // \ \3 3 // \ \3 3 //
$$\left(\left(\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right)$$
=
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| |1 I*\/ 2 || | |1 I*\/ 2 || / / ___\\ / / ___\\ | |1 I*\/ 2 || | |1 I*\/ 2 || / / ___\\ / / ___\\
- 2*re|atan|- - -------|| - 2*re|atan|- + -------|| + 2*re\atan\1 + I*\/ 2 // + 2*re\atan\1 - I*\/ 2 // - 2*I*im|atan|- - -------|| - 2*I*im|atan|- + -------|| + 2*I*im\atan\1 + I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 //
\ \3 3 // \ \3 3 // \ \3 3 // \ \3 3 //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}$$
producto
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ | | |1 I*\/ 2 || | |1 I*\/ 2 ||| | | |1 I*\/ 2 || | |1 I*\/ 2 ||| / / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ |- 2*re|atan|- - -------|| - 2*I*im|atan|- - -------|||*|- 2*re|atan|- + -------|| - 2*I*im|atan|- + -------|||*\2*re\atan\1 - I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 ///*\2*re\atan\1 + I*\/ 2 // + 2*I*im\atan\1 + I*\/ 2 /// \ \ \3 3 // \ \3 3 /// \ \ \3 3 // \ \3 3 ///
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right)$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ | | |1 I*\/ 2 || | |1 I*\/ 2 ||| | | |1 I*\/ 2 || | |1 I*\/ 2 |||
16*\I*im\atan\1 + I*\/ 2 // + re\atan\1 + I*\/ 2 ///*\I*im\atan\1 - I*\/ 2 // + re\atan\1 - I*\/ 2 ///*|I*im|atan|- - -------|| + re|atan|- - -------|||*|I*im|atan|- + -------|| + re|atan|- + -------|||
\ \ \3 3 // \ \3 3 /// \ \ \3 3 // \ \3 3 ///
$$16 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right)$$
16*(i*im(atan(1 + i*sqrt(2))) + re(atan(1 + i*sqrt(2))))*(i*im(atan(1 - i*sqrt(2))) + re(atan(1 - i*sqrt(2))))*(i*im(atan(1/3 - i*sqrt(2)/3)) + re(atan(1/3 - i*sqrt(2)/3)))*(i*im(atan(1/3 + i*sqrt(2)/3)) + re(atan(1/3 + i*sqrt(2)/3)))
Respuesta numérica
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x1 = -0.785398163397448 + 0.881373587019543*i
x2 = -0.785398163397448 - 0.881373587019543*i
x3 = 2.35619449019234 - 0.881373587019543*i
x4 = 2.35619449019234 + 0.881373587019543*i
x4 = 2.35619449019234 + 0.881373587019543*i