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- La ecuación:
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- Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
- ln(y^ dos -x^ dos + tres)
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- ln(y2-x2+3)
- lny2-x2+3
- ln(y²-x²+3)
- ln(y en el grado 2-x en el grado 2+3)
- lny^2-x^2+3
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Expresiones semejantes
- ln(y^2-x^2-3)
- ln(y^2+x^2+3)
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Expresiones con funciones
- ln
- ln(101,3/x)=17,47/8,314*(1/268,15-1/192,15)
- ln(-p+1)-ln(p)
- ln((2x)/(x-4))-x=0
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- lnx+1=0
ln(y^2-x^2+3) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 2 \ log\y - x + 3/ = 0
$$\log{\left(\left(- x^{2} + y^{2}\right) + 3 \right)} = 0$$
Gráfica
Suma y producto de raíces
[src]
suma
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/| 4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/| 4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/| 4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/|
- \/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *cos|------------------------------------------| - I*\/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *sin|------------------------------------------| + \/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *cos|------------------------------------------| + I*\/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *sin|------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ ___________________________________________ ___________________________________________ \ / ___________________________________________ ___________________________________________ \ | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | 4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/| 4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/|| |4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/| 4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/|| |- \/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *cos|------------------------------------------| - I*\/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *sin|------------------------------------------||*|\/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *cos|------------------------------------------| + I*\/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *sin|------------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)}\right)$$
=
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/ 2 / 2 2 \
/ / 2 2 \ 2 2 I*atan2\2*im(x)*re(x), -2 + re (x) - im (x)/
-\/ \2 + im (x) - re (x)/ + 4*im (x)*re (x) *e
$$- \sqrt{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}$$
-sqrt((2 + im(x)^2 - re(x)^2)^2 + 4*im(x)^2*re(x)^2)*exp(i*atan2(2*im(x)*re(x), -2 + re(x)^2 - im(x)^2))
Respuesta rápida
[src]
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/| 4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/|
y1 = - \/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *cos|------------------------------------------| - I*\/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *sin|------------------------------------------|
\ 2 / \ 2 /
$$y_{1} = - i \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)}$$
___________________________________________ ___________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/| 4 / / 2 2 \ 2 2 |atan2\2*im(x)*re(x), -2 + re (x) - im (x)/|
y2 = \/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *cos|------------------------------------------| + I*\/ \-2 + re (x) - im (x)/ + 4*im (x)*re (x) *sin|------------------------------------------|
\ 2 / \ 2 /
$$y_{2} = i \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \right)}}{2} \right)}$$
y2 = i*((re(x)^2 - im(x)^2 - 2)^2 + 4*re(x)^2*im(x)^2)^(1/4)*sin(atan2(2*re(x)*im(x, re(x)^2 - im(x)^2 - 2)/2) + ((re(x)^2 - im(x)^2 - 2)^2 + 4*re(x)^2*im(x)^2)^(1/4)*cos(atan2(2*re(x)*im(x), re(x)^2 - im(x)^2 - 2)/2))