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Expresiones idénticas
- sqrty*d*y=3sqrtx*d*x
- raíz cuadrada de y multiplicar por d multiplicar por y es igual a 3 raíz cuadrada de x multiplicar por d multiplicar por x
- √y*d*y=3√x*d*x
- sqrtydy=3sqrtxdx
sqrty*d*y=3sqrtx*d*x la ecuación
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Solución
Gráfica
Respuesta rápida
[src]
2/3 2/3 y1 = 3 *re(x) + I*3 *im(x)
$$y_{1} = 3^{\frac{2}{3}} \operatorname{re}{\left(x\right)} + 3^{\frac{2}{3}} i \operatorname{im}{\left(x\right)}$$
/ 2\ / 2\
| / 3 ___ 5/6\ | | / 3 ___ 5/6\ |
| | \/ 3 I*3 | | | | \/ 3 I*3 | |
y2 = I*im|x*|- ----- - ------| | + re|x*|- ----- - ------| |
\ \ 2 2 / / \ \ 2 2 / /
$$y_{2} = \operatorname{re}{\left(x \left(- \frac{\sqrt[3]{3}}{2} - \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)} + i \operatorname{im}{\left(x \left(- \frac{\sqrt[3]{3}}{2} - \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)}$$
/ 2\ / 2\
| / 3 ___ 5/6\ | | / 3 ___ 5/6\ |
| | \/ 3 I*3 | | | | \/ 3 I*3 | |
y3 = I*im|x*|- ----- + ------| | + re|x*|- ----- + ------| |
\ \ 2 2 / / \ \ 2 2 / /
$$y_{3} = \operatorname{re}{\left(x \left(- \frac{\sqrt[3]{3}}{2} + \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)} + i \operatorname{im}{\left(x \left(- \frac{\sqrt[3]{3}}{2} + \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)}$$
y3 = re(x*(-3^(1/3)/2 + 3^(5/6)*i/2)^2) + i*im(x*(-3^(1/3)/2 + 3^(5/6)*i/2)^2)
Suma y producto de raíces
[src]
suma
/ 2\ / 2\ / 2\ / 2\
| / 3 ___ 5/6\ | | / 3 ___ 5/6\ | | / 3 ___ 5/6\ | | / 3 ___ 5/6\ |
2/3 2/3 | | \/ 3 I*3 | | | | \/ 3 I*3 | | | | \/ 3 I*3 | | | | \/ 3 I*3 | |
3 *re(x) + I*3 *im(x) + I*im|x*|- ----- - ------| | + re|x*|- ----- - ------| | + I*im|x*|- ----- + ------| | + re|x*|- ----- + ------| |
\ \ 2 2 / / \ \ 2 2 / / \ \ 2 2 / / \ \ 2 2 / /
$$\left(\left(3^{\frac{2}{3}} \operatorname{re}{\left(x\right)} + 3^{\frac{2}{3}} i \operatorname{im}{\left(x\right)}\right) + \left(\operatorname{re}{\left(x \left(- \frac{\sqrt[3]{3}}{2} - \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)} + i \operatorname{im}{\left(x \left(- \frac{\sqrt[3]{3}}{2} - \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)}\right)\right) + \left(\operatorname{re}{\left(x \left(- \frac{\sqrt[3]{3}}{2} + \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)} + i \operatorname{im}{\left(x \left(- \frac{\sqrt[3]{3}}{2} + \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)}\right)$$
=
/ 2\ / 2\ / 2\ / 2\
| / 3 ___ 5/6\ | | / 3 ___ 5/6\ | | / 3 ___ 5/6\ | | / 3 ___ 5/6\ |
| | \/ 3 I*3 | | | | \/ 3 I*3 | | 2/3 2/3 | | \/ 3 I*3 | | | | \/ 3 I*3 | |
I*im|x*|- ----- + ------| | + I*im|x*|- ----- - ------| | + 3 *re(x) + I*3 *im(x) + re|x*|- ----- + ------| | + re|x*|- ----- - ------| |
\ \ 2 2 / / \ \ 2 2 / / \ \ 2 2 / / \ \ 2 2 / /
$$3^{\frac{2}{3}} \operatorname{re}{\left(x\right)} + \operatorname{re}{\left(x \left(- \frac{\sqrt[3]{3}}{2} - \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)} + \operatorname{re}{\left(x \left(- \frac{\sqrt[3]{3}}{2} + \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)} + 3^{\frac{2}{3}} i \operatorname{im}{\left(x\right)} + i \operatorname{im}{\left(x \left(- \frac{\sqrt[3]{3}}{2} - \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)} + i \operatorname{im}{\left(x \left(- \frac{\sqrt[3]{3}}{2} + \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)}$$
producto
/ / 2\ / 2\\ / / 2\ / 2\\
| | / 3 ___ 5/6\ | | / 3 ___ 5/6\ || | | / 3 ___ 5/6\ | | / 3 ___ 5/6\ ||
/ 2/3 2/3 \ | | | \/ 3 I*3 | | | | \/ 3 I*3 | || | | | \/ 3 I*3 | | | | \/ 3 I*3 | ||
\3 *re(x) + I*3 *im(x)/*|I*im|x*|- ----- - ------| | + re|x*|- ----- - ------| ||*|I*im|x*|- ----- + ------| | + re|x*|- ----- + ------| ||
\ \ \ 2 2 / / \ \ 2 2 / // \ \ \ 2 2 / / \ \ 2 2 / //
$$\left(3^{\frac{2}{3}} \operatorname{re}{\left(x\right)} + 3^{\frac{2}{3}} i \operatorname{im}{\left(x\right)}\right) \left(\operatorname{re}{\left(x \left(- \frac{\sqrt[3]{3}}{2} - \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)} + i \operatorname{im}{\left(x \left(- \frac{\sqrt[3]{3}}{2} - \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)}\right) \left(\operatorname{re}{\left(x \left(- \frac{\sqrt[3]{3}}{2} + \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)} + i \operatorname{im}{\left(x \left(- \frac{\sqrt[3]{3}}{2} + \frac{3^{\frac{5}{6}} i}{2}\right)^{2}\right)}\right)$$
=
3 2 3 2 9*re (x) - 27*im (x)*re(x) - 9*I*im (x) + 27*I*re (x)*im(x)
$$9 \left(\operatorname{re}{\left(x\right)}\right)^{3} + 27 i \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(x\right)} - 27 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 9 i \left(\operatorname{im}{\left(x\right)}\right)^{3}$$
9*re(x)^3 - 27*im(x)^2*re(x) - 9*i*im(x)^3 + 27*i*re(x)^2*im(x)