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- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 3*x=8
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Ecuación 9-7(x+3)=5-6x
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Ecuación 4x-5=3+2(x+1)
- Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
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- f multiplicar por (x) menos dos multiplicar por x menos uno dividir por seis multiplicar por x en el grado tres es igual a cero
- f*(x)-2*x-1/6*x3=0
- f*x-2*x-1/6*x3=0
- f*(x)-2*x-1/6*x³=0
- f*(x)-2*x-1/6*x en el grado 3=0
- f(x)-2x-1/6x^3=0
- f(x)-2x-1/6x3=0
- fx-2x-1/6x3=0
- fx-2x-1/6x^3=0
- f*(x)-2*x-1/6*x^3=O
- f*(x)-2*x-1 dividir por 6*x^3=0
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Expresiones semejantes
- f*(x)+2*x-1/6*x^3=0
- f*(x)-2*x+1/6*x^3=0
f*(x)-2*x-1/6*x^3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Teorema de Cardano-Vieta
reescribamos la ecuación
$$- \frac{x^{3}}{6} + \left(f x - 2 x\right) = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$- 6 f x + x^{3} + 12 x = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 12 - 6 f$$
$$v = \frac{d}{a}$$
$$v = 0$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 12 - 6 f$$
$$x_{1} x_{2} x_{3} = 0$$
$$- \frac{x^{3}}{6} + \left(f x - 2 x\right) = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$- 6 f x + x^{3} + 12 x = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 12 - 6 f$$
$$v = \frac{d}{a}$$
$$v = 0$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 12 - 6 f$$
$$x_{1} x_{2} x_{3} = 0$$
Gráfica
Suma y producto de raíces
[src]
suma
________________________ ________________________ ________________________ ________________________
___ 4 / 2 2 /atan2(im(f), -2 + re(f))\ ___ 4 / 2 2 /atan2(im(f), -2 + re(f))\ ___ 4 / 2 2 /atan2(im(f), -2 + re(f))\ ___ 4 / 2 2 /atan2(im(f), -2 + re(f))\
- \/ 6 *\/ (-2 + re(f)) + im (f) *cos|------------------------| - I*\/ 6 *\/ (-2 + re(f)) + im (f) *sin|------------------------| + \/ 6 *\/ (-2 + re(f)) + im (f) *cos|------------------------| + I*\/ 6 *\/ (-2 + re(f)) + im (f) *sin|------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- \sqrt{6} i \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)} - \sqrt{6} \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)}\right) + \left(\sqrt{6} i \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)} + \sqrt{6} \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ ________________________ ________________________ \ / ________________________ ________________________ \ | ___ 4 / 2 2 /atan2(im(f), -2 + re(f))\ ___ 4 / 2 2 /atan2(im(f), -2 + re(f))\| | ___ 4 / 2 2 /atan2(im(f), -2 + re(f))\ ___ 4 / 2 2 /atan2(im(f), -2 + re(f))\| 0*|- \/ 6 *\/ (-2 + re(f)) + im (f) *cos|------------------------| - I*\/ 6 *\/ (-2 + re(f)) + im (f) *sin|------------------------||*|\/ 6 *\/ (-2 + re(f)) + im (f) *cos|------------------------| + I*\/ 6 *\/ (-2 + re(f)) + im (f) *sin|------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$0 \left(- \sqrt{6} i \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)} - \sqrt{6} \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)}\right) \left(\sqrt{6} i \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)} + \sqrt{6} \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)}\right)$$
=
0
$$0$$
0
Respuesta rápida
[src]
x1 = 0
$$x_{1} = 0$$
________________________ ________________________
___ 4 / 2 2 /atan2(im(f), -2 + re(f))\ ___ 4 / 2 2 /atan2(im(f), -2 + re(f))\
x2 = - \/ 6 *\/ (-2 + re(f)) + im (f) *cos|------------------------| - I*\/ 6 *\/ (-2 + re(f)) + im (f) *sin|------------------------|
\ 2 / \ 2 /
$$x_{2} = - \sqrt{6} i \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)} - \sqrt{6} \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)}$$
________________________ ________________________
___ 4 / 2 2 /atan2(im(f), -2 + re(f))\ ___ 4 / 2 2 /atan2(im(f), -2 + re(f))\
x3 = \/ 6 *\/ (-2 + re(f)) + im (f) *cos|------------------------| + I*\/ 6 *\/ (-2 + re(f)) + im (f) *sin|------------------------|
\ 2 / \ 2 /
$$x_{3} = \sqrt{6} i \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)} + \sqrt{6} \sqrt[4]{\left(\operatorname{re}{\left(f\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(f\right)},\operatorname{re}{\left(f\right)} - 2 \right)}}{2} \right)}$$
x3 = sqrt(6)*i*((re(f) - 2)^2 + im(f)^2)^(1/4)*sin(atan2(im(f, re(f) - 2)/2) + sqrt(6)*((re(f) - 2)^2 + im(f)^2)^(1/4)*cos(atan2(im(f), re(f) - 2)/2))