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- La ecuación:
-
Ecuación 5*x=32+x
-
Ecuación 4*x-8=x+1
-
Ecuación 3*x^2+13*x-10=0
-
Ecuación 8-x^2=0
- Expresar {x} en función de y en la ecuación:
- -6*x+11*y=-5
- -15*x+7*y=1
- -11*x-11*y=4
- 11*x-9*y=-4
- Derivada de:
- f*(x)
-
x^3
- Límite de la función:
-
x^3
- Gráfico de la función y =:
-
x^3
-
Expresiones idénticas
- f*(x)=x^ tres
- f multiplicar por (x) es igual a x al cubo
- f multiplicar por (x) es igual a x en el grado tres
- f*(x)=x3
- f*x=x3
- f*(x)=x³
- f*(x)=x en el grado 3
- f(x)=x^3
- f(x)=x3
- fx=x3
- fx=x^3
-
Expresiones semejantes
- f*x=x^7-4*x^5+2*x-1
f*(x)=x^3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Teorema de Cardano-Vieta
reescribamos la ecuación
$$f x = x^{3}$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$- f x + x^{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - f$$
$$v = \frac{d}{a}$$
$$v = 0$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - f$$
$$x_{1} x_{2} x_{3} = 0$$
$$f x = x^{3}$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$- f x + x^{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - f$$
$$v = \frac{d}{a}$$
$$v = 0$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - f$$
$$x_{1} x_{2} x_{3} = 0$$
Gráfica
Suma y producto de raíces
[src]
suma
_________________ _________________ _________________ _________________
4 / 2 2 /atan2(im(f), re(f))\ 4 / 2 2 /atan2(im(f), re(f))\ 4 / 2 2 /atan2(im(f), re(f))\ 4 / 2 2 /atan2(im(f), re(f))\
- \/ im (f) + re (f) *cos|-------------------| - I*\/ im (f) + re (f) *sin|-------------------| + \/ im (f) + re (f) *cos|-------------------| + I*\/ im (f) + re (f) *sin|-------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ _________________ _________________ \ / _________________ _________________ \ | 4 / 2 2 /atan2(im(f), re(f))\ 4 / 2 2 /atan2(im(f), re(f))\| |4 / 2 2 /atan2(im(f), re(f))\ 4 / 2 2 /atan2(im(f), re(f))\| 0*|- \/ im (f) + re (f) *cos|-------------------| - I*\/ im (f) + re (f) *sin|-------------------||*|\/ im (f) + re (f) *cos|-------------------| + I*\/ im (f) + re (f) *sin|-------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$0 \left(- i \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)}\right)$$
=
0
$$0$$
0
Respuesta rápida
[src]
x1 = 0
$$x_{1} = 0$$
_________________ _________________
4 / 2 2 /atan2(im(f), re(f))\ 4 / 2 2 /atan2(im(f), re(f))\
x2 = - \/ im (f) + re (f) *cos|-------------------| - I*\/ im (f) + re (f) *sin|-------------------|
\ 2 / \ 2 /
$$x_{2} = - i \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)}$$
_________________ _________________
4 / 2 2 /atan2(im(f), re(f))\ 4 / 2 2 /atan2(im(f), re(f))\
x3 = \/ im (f) + re (f) *cos|-------------------| + I*\/ im (f) + re (f) *sin|-------------------|
\ 2 / \ 2 /
$$x_{3} = i \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} \right)}}{2} \right)}$$
x3 = i*(re(f)^2 + im(f)^2)^(1/4)*sin(atan2(im(f, re(f))/2) + (re(f)^2 + im(f)^2)^(1/4)*cos(atan2(im(f), re(f))/2))