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- La ecuación:
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Ecuación x^4+2*x^2-8=0
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Ecuación x*(x^2+8*x+16)=5*(x+4)
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Ecuación -25-x=-17
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Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
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Expresiones idénticas
- (tres /(x+y- uno))+(uno /(dos *x-y+ tres))+(siete / cinco)= cero
- (3 dividir por (x más y menos 1)) más (1 dividir por (2 multiplicar por x menos y más 3)) más (7 dividir por 5) es igual a 0
- (tres dividir por (x más y menos uno)) más (uno dividir por (dos multiplicar por x menos y más tres)) más (siete dividir por cinco) es igual a cero
- (3/(x+y-1))+(1/(2x-y+3))+(7/5)=0
- 3/x+y-1+1/2x-y+3+7/5=0
- (3/(x+y-1))+(1/(2*x-y+3))+(7/5)=O
- (3 dividir por (x+y-1))+(1 dividir por (2*x-y+3))+(7 dividir por 5)=0
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Expresiones semejantes
- (3/(x-y-1))+(1/(2*x-y+3))+(7/5)=0
- (3/(x+y+1))+(1/(2*x-y+3))+(7/5)=0
- (3/(x+y-1))+(1/(2*x-y+3))-(7/5)=0
- (3/(x+y-1))-(1/(2*x-y+3))+(7/5)=0
- (3/(x+y-1))+(1/(2*x-y-3))+(7/5)=0
- (3/(x+y-1))+(1/(2*x+y+3))+(7/5)=0
(3/(x+y-1))+(1/(2*x-y+3))+(7/5)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 1 7 --------- + ----------- + - = 0 x + y - 1 2*x - y + 3 5
$$\left(\frac{1}{\left(2 x - y\right) + 3} + \frac{3}{\left(x + y\right) - 1}\right) + \frac{7}{5} = 0$$
Solución detallada
Tenemos la ecuación:
$$\left(\frac{1}{\left(2 x - y\right) + 3} + \frac{3}{\left(x + y\right) - 1}\right) + \frac{7}{5} = 0$$
Multipliquemos las dos partes de la ecuación por los denominadores:
-1 + x + y y 3 - y + 2*x
obtendremos:
$$\left(\left(\frac{1}{\left(2 x - y\right) + 3} + \frac{3}{\left(x + y\right) - 1}\right) + \frac{7}{5}\right) \left(x + y - 1\right) = 0$$
$$\frac{35 x - 10 y + 7 \left(x + y - 1\right) \left(2 x - y + 3\right) + 40}{5 \left(2 x - y + 3\right)} = 0$$
$$\frac{35 x - 10 y + 7 \left(x + y - 1\right) \left(2 x - y + 3\right) + 40}{5 \left(2 x - y + 3\right)} \left(2 x - y + 3\right) = 0 \left(2 x - y + 3\right)$$
$$\frac{14 x^{2}}{5} + \frac{7 x y}{5} + \frac{42 x}{5} - \frac{7 y^{2}}{5} + \frac{18 y}{5} + \frac{19}{5} = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \frac{14}{5}$$
$$b = \frac{7 y}{5} + \frac{42}{5}$$
$$c = - \frac{7 y^{2}}{5} + \frac{18 y}{5} + \frac{19}{5}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = - \frac{y}{4} + \frac{5 \sqrt{\frac{392 y^{2}}{25} - \frac{1008 y}{25} + \left(\frac{7 y}{5} + \frac{42}{5}\right)^{2} - \frac{1064}{25}}}{28} - \frac{3}{2}$$
$$x_{2} = - \frac{y}{4} - \frac{5 \sqrt{\frac{392 y^{2}}{25} - \frac{1008 y}{25} + \left(\frac{7 y}{5} + \frac{42}{5}\right)^{2} - \frac{1064}{25}}}{28} - \frac{3}{2}$$
$$\left(\frac{1}{\left(2 x - y\right) + 3} + \frac{3}{\left(x + y\right) - 1}\right) + \frac{7}{5} = 0$$
Multipliquemos las dos partes de la ecuación por los denominadores:
-1 + x + y y 3 - y + 2*x
obtendremos:
$$\left(\left(\frac{1}{\left(2 x - y\right) + 3} + \frac{3}{\left(x + y\right) - 1}\right) + \frac{7}{5}\right) \left(x + y - 1\right) = 0$$
$$\frac{35 x - 10 y + 7 \left(x + y - 1\right) \left(2 x - y + 3\right) + 40}{5 \left(2 x - y + 3\right)} = 0$$
$$\frac{35 x - 10 y + 7 \left(x + y - 1\right) \left(2 x - y + 3\right) + 40}{5 \left(2 x - y + 3\right)} \left(2 x - y + 3\right) = 0 \left(2 x - y + 3\right)$$
$$\frac{14 x^{2}}{5} + \frac{7 x y}{5} + \frac{42 x}{5} - \frac{7 y^{2}}{5} + \frac{18 y}{5} + \frac{19}{5} = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \frac{14}{5}$$
$$b = \frac{7 y}{5} + \frac{42}{5}$$
$$c = - \frac{7 y^{2}}{5} + \frac{18 y}{5} + \frac{19}{5}$$
, entonces
D = b^2 - 4 * a * c =
(42/5 + 7*y/5)^2 - 4 * (14/5) * (19/5 - 7*y^2/5 + 18*y/5) = -1064/25 + (42/5 + 7*y/5)^2 - 1008*y/25 + 392*y^2/25
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = - \frac{y}{4} + \frac{5 \sqrt{\frac{392 y^{2}}{25} - \frac{1008 y}{25} + \left(\frac{7 y}{5} + \frac{42}{5}\right)^{2} - \frac{1064}{25}}}{28} - \frac{3}{2}$$
$$x_{2} = - \frac{y}{4} - \frac{5 \sqrt{\frac{392 y^{2}}{25} - \frac{1008 y}{25} + \left(\frac{7 y}{5} + \frac{42}{5}\right)^{2} - \frac{1064}{25}}}{28} - \frac{3}{2}$$
Gráfica
Respuesta rápida
[src]
/ ________________________________________________________________________________ \ ________________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|| 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|
| \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *sin|------------------------------------------------------------------------------|| \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *cos|------------------------------------------------------------------------------|
3 re(y) | im(y) \ 2 /| \ 2 /
x1 = - - - ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 4 \ 4 28 / 28
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}$$
/ ________________________________________________________________________________ \ ________________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|| 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|
| \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *sin|------------------------------------------------------------------------------|| \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *cos|------------------------------------------------------------------------------|
3 re(y) | im(y) \ 2 /| \ 2 /
x2 = - - - ----- + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 4 \ 4 28 / 28
$$x_{2} = i \left(\frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}$$
x2 = i*(((882*re(y)*im(y) - 420*im(y))^2 + (441*re(y)^2 - 420*re(y) - 441*im(y)^2 + 700)^2)^(1/4)*sin(atan2(882*re(y)*im(y) - 420*im(y, 441*re(y)^2 - 420*re(y) - 441*im(y)^2 + 700)/2)/28 - im(y)/4) + ((882*re(y)*im(y) - 420*im(y))^2 + (441*re(y)^2 - 420*re(y) - 441*im(y)^2 + 700)^2)^(1/4)*cos(atan2(882*re(y)*im(y) - 420*im(y), 441*re(y)^2 - 420*re(y) - 441*im(y)^2 + 700)/2)/28 - re(y)/4 - 3/2)
Suma y producto de raíces
[src]
suma
/ ________________________________________________________________________________ \ ________________________________________________________________________________ / ________________________________________________________________________________ \ ________________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|| 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/| | 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|| 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|
| \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *sin|------------------------------------------------------------------------------|| \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *cos|------------------------------------------------------------------------------| | \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *sin|------------------------------------------------------------------------------|| \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *cos|------------------------------------------------------------------------------|
3 re(y) | im(y) \ 2 /| \ 2 / 3 re(y) | im(y) \ 2 /| \ 2 /
- - - ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + - - - ----- + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 4 \ 4 28 / 28 2 4 \ 4 28 / 28
$$\left(i \left(- \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}\right) + \left(i \left(\frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}\right)$$
=
/ ________________________________________________________________________________ \ / ________________________________________________________________________________ \
| / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|| | 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/||
| \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *sin|------------------------------------------------------------------------------|| | \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *sin|------------------------------------------------------------------------------||
re(y) | im(y) \ 2 /| | im(y) \ 2 /|
-3 - ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
2 \ 4 28 / \ 4 28 /
$$i \left(- \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) + i \left(\frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} - 3$$
producto
/ / ________________________________________________________________________________ \ ________________________________________________________________________________ \ / / ________________________________________________________________________________ \ ________________________________________________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|| 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|| | | 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|| 4 / 2 / 2 2 \ |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|| | | \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *sin|------------------------------------------------------------------------------|| \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *cos|------------------------------------------------------------------------------|| | | \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *sin|------------------------------------------------------------------------------|| \/ (-420*im(y) + 882*im(y)*re(y)) + \700 - 441*im (y) - 420*re(y) + 441*re (y)/ *cos|------------------------------------------------------------------------------|| | 3 re(y) | im(y) \ 2 /| \ 2 /| | 3 re(y) | im(y) \ 2 /| \ 2 /| |- - - ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|- - - ----- + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 2 4 \ 4 28 / 28 / \ 2 4 \ 4 28 / 28 /
$$\left(i \left(- \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}\right) \left(i \left(\frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}\right)$$
=
2 2 19 im (y) re (y) 9*re(y) 9*I*im(y) -- + ------ - ------ + ------- + --------- - I*im(y)*re(y) 14 2 2 7 7
$$- \frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{2} - i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \frac{9 \operatorname{re}{\left(y\right)}}{7} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{2} + \frac{9 i \operatorname{im}{\left(y\right)}}{7} + \frac{19}{14}$$
19/14 + im(y)^2/2 - re(y)^2/2 + 9*re(y)/7 + 9*i*im(y)/7 - i*im(y)*re(y)