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- La ecuación:
-
Ecuación 5x+15=x-1
-
Ecuación 3x^2=0
- Ecuación x^2-49=0
-
Ecuación 1-x/2=x/3
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- 9*x+17*y=13
- -19*x+14*y=20
-
Expresiones idénticas
- u=arctg((x+y)/(uno -xy))
- u es igual a arctg((x más y) dividir por (1 menos xy))
- u es igual a arctg((x más y) dividir por (uno menos xy))
- u=arctgx+y/1-xy
- u=arctg((x+y) dividir por (1-xy))
-
Expresiones semejantes
- u=arctg((x-y)/(1-xy))
- u=arctg((x+y)/(1+xy))
-
Expresiones con funciones
- arctg
- arctg(x)=1
- arctg(x)=pi/3
- xy
- xy+y=ex,
- xy^2-y^3=4x-5
- xy=4Scrt(2x^2+y^2+y)
- xy=2y
- xyy=lnx
u=arctg((x+y)/(1-xy)) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ x + y \
u = atan|-------|
\1 - x*y/
$$u = \operatorname{atan}{\left(\frac{x + y}{- x y + 1} \right)}$$
Gráfica
Suma y producto de raíces
[src]
suma
/ / sinh(2*im(u)) \ / sin(2*re(u)) \ \ / sin(2*re(u)) \ / sinh(2*im(u)) \ |(1 + re(x*tan(u)))*|-im(x) + ----------------------------| |-re(x) + ----------------------------|*im(x*tan(u))| (1 + re(x*tan(u)))*|-re(x) + ----------------------------| |-im(x) + ----------------------------|*im(x*tan(u)) | \ cos(2*re(u)) + cosh(2*im(u))/ \ cos(2*re(u)) + cosh(2*im(u))/ | \ cos(2*re(u)) + cosh(2*im(u))/ \ cos(2*re(u)) + cosh(2*im(u))/ I*|---------------------------------------------------------- - ----------------------------------------------------| + ---------------------------------------------------------- + ---------------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ (1 + re(x*tan(u))) + im (x*tan(u)) (1 + re(x*tan(u))) + im (x*tan(u)) / (1 + re(x*tan(u))) + im (x*tan(u)) (1 + re(x*tan(u))) + im (x*tan(u))
$$i \left(- \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right) \left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}$$
=
/ / sinh(2*im(u)) \ / sin(2*re(u)) \ \ / sin(2*re(u)) \ / sinh(2*im(u)) \ |(1 + re(x*tan(u)))*|-im(x) + ----------------------------| |-re(x) + ----------------------------|*im(x*tan(u))| (1 + re(x*tan(u)))*|-re(x) + ----------------------------| |-im(x) + ----------------------------|*im(x*tan(u)) | \ cos(2*re(u)) + cosh(2*im(u))/ \ cos(2*re(u)) + cosh(2*im(u))/ | \ cos(2*re(u)) + cosh(2*im(u))/ \ cos(2*re(u)) + cosh(2*im(u))/ I*|---------------------------------------------------------- - ----------------------------------------------------| + ---------------------------------------------------------- + ---------------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ (1 + re(x*tan(u))) + im (x*tan(u)) (1 + re(x*tan(u))) + im (x*tan(u)) / (1 + re(x*tan(u))) + im (x*tan(u)) (1 + re(x*tan(u))) + im (x*tan(u))
$$i \left(- \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right) \left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}$$
producto
/ / sinh(2*im(u)) \ / sin(2*re(u)) \ \ / sin(2*re(u)) \ / sinh(2*im(u)) \ |(1 + re(x*tan(u)))*|-im(x) + ----------------------------| |-re(x) + ----------------------------|*im(x*tan(u))| (1 + re(x*tan(u)))*|-re(x) + ----------------------------| |-im(x) + ----------------------------|*im(x*tan(u)) | \ cos(2*re(u)) + cosh(2*im(u))/ \ cos(2*re(u)) + cosh(2*im(u))/ | \ cos(2*re(u)) + cosh(2*im(u))/ \ cos(2*re(u)) + cosh(2*im(u))/ I*|---------------------------------------------------------- - ----------------------------------------------------| + ---------------------------------------------------------- + ---------------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ (1 + re(x*tan(u))) + im (x*tan(u)) (1 + re(x*tan(u))) + im (x*tan(u)) / (1 + re(x*tan(u))) + im (x*tan(u)) (1 + re(x*tan(u))) + im (x*tan(u))
$$i \left(- \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right) \left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}$$
=
-((1 + re(x*tan(u)))*(-sin(2*re(u)) + (cos(2*re(u)) + cosh(2*im(u)))*re(x)) + (-sinh(2*im(u)) + (cos(2*re(u)) + cosh(2*im(u)))*im(x))*im(x*tan(u)) - I*((-sin(2*re(u)) + (cos(2*re(u)) + cosh(2*im(u)))*re(x))*im(x*tan(u)) - (1 + re(x*tan(u)))*(-sinh(2*im(u)) + (cos(2*re(u)) + cosh(2*im(u)))*im(x))))
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2 2 \
\(1 + re(x*tan(u))) + im (x*tan(u))/*(cos(2*re(u)) + cosh(2*im(u)))
$$- \frac{- i \left(\left(\left(\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \operatorname{re}{\left(x\right)} - \sin{\left(2 \operatorname{re}{\left(u\right)} \right)}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)} - \left(\left(\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \operatorname{im}{\left(x\right)} - \sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)\right) + \left(\left(\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \operatorname{re}{\left(x\right)} - \sin{\left(2 \operatorname{re}{\left(u\right)} \right)}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right) + \left(\left(\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \operatorname{im}{\left(x\right)} - \sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}\right) \left(\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right)}$$
-((1 + re(x*tan(u)))*(-sin(2*re(u)) + (cos(2*re(u)) + cosh(2*im(u)))*re(x)) + (-sinh(2*im(u)) + (cos(2*re(u)) + cosh(2*im(u)))*im(x))*im(x*tan(u)) - i*((-sin(2*re(u)) + (cos(2*re(u)) + cosh(2*im(u)))*re(x))*im(x*tan(u)) - (1 + re(x*tan(u)))*(-sinh(2*im(u)) + (cos(2*re(u)) + cosh(2*im(u)))*im(x))))/(((1 + re(x*tan(u)))^2 + im(x*tan(u))^2)*(cos(2*re(u)) + cosh(2*im(u))))
Respuesta rápida
[src]
/ / sinh(2*im(u)) \ / sin(2*re(u)) \ \ / sin(2*re(u)) \ / sinh(2*im(u)) \
|(1 + re(x*tan(u)))*|-im(x) + ----------------------------| |-re(x) + ----------------------------|*im(x*tan(u))| (1 + re(x*tan(u)))*|-re(x) + ----------------------------| |-im(x) + ----------------------------|*im(x*tan(u))
| \ cos(2*re(u)) + cosh(2*im(u))/ \ cos(2*re(u)) + cosh(2*im(u))/ | \ cos(2*re(u)) + cosh(2*im(u))/ \ cos(2*re(u)) + cosh(2*im(u))/
y1 = I*|---------------------------------------------------------- - ----------------------------------------------------| + ---------------------------------------------------------- + ----------------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ (1 + re(x*tan(u))) + im (x*tan(u)) (1 + re(x*tan(u))) + im (x*tan(u)) / (1 + re(x*tan(u))) + im (x*tan(u)) (1 + re(x*tan(u))) + im (x*tan(u))
$$y_{1} = i \left(- \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right) \left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}$$
y1 = i*(-(-re(x) + sin(2*re(u))/(cos(2*re(u)) + cosh(2*im(u))))*im(x*tan(u))/((re(x*tan(u)) + 1)^2 + im(x*tan(u))^2) + (re(x*tan(u)) + 1)*(-im(x) + sinh(2*im(u))/(cos(2*re(u)) + cosh(2*im(u))))/((re(x*tan(u)) + 1)^2 + im(x*tan(u))^2)) + (-re(x) + sin(2*re(u))/(cos(2*re(u)) + cosh(2*im(u))))*(re(x*tan(u)) + 1)/((re(x*tan(u)) + 1)^2 + im(x*tan(u))^2) + (-im(x) + sinh(2*im(u))/(cos(2*re(u)) + cosh(2*im(u))))*im(x*tan(u))/((re(x*tan(u)) + 1)^2 + im(x*tan(u))^2)