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- La ecuación:
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Ecuación x^2+x+1=0
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Ecuación 5*x=32+x
-
Ecuación 4*x-8=x+1
-
Ecuación (x-1)(x+9)=8x
- Expresar {x} en función de y en la ecuación:
- -18*x-8*y=-18
- -13*x+12*y=-19
- -1*x+11*y=-9
- 4*x-4*y=-19
- Gráfico de la función y =:
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x^3-3*x+5
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Expresiones idénticas
- x^ tres - tres *x+ cinco = cero
- x al cubo menos 3 multiplicar por x más 5 es igual a 0
- x en el grado tres menos tres multiplicar por x más cinco es igual a cero
- x3-3*x+5=0
- x³-3*x+5=0
- x en el grado 3-3*x+5=0
- x^3-3x+5=0
- x3-3x+5=0
- x^3-3*x+5=O
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Expresiones semejantes
- x^3-3*x-5=0
- x^3+3*x+5=0
x^3-3*x+5=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -3$$
$$v = \frac{d}{a}$$
$$v = 5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -3$$
$$x_{1} x_{2} x_{3} = 5$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -3$$
$$v = \frac{d}{a}$$
$$v = 5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -3$$
$$x_{1} x_{2} x_{3} = 5$$
Respuesta rápida
[src]
_________________ / _________________\
/ ____ | / ____ |
/ 135 27*\/ 21 | ___ / 135 27*\/ 21 |
3 / --- + --------- | ___ \/ 3 *3 / --- + --------- |
\/ 2 2 3 | 3*\/ 3 \/ 2 2 |
x1 = ---------------------- + ------------------------ + I*|- ------------------------ + ----------------------------|
6 _________________ | _________________ 6 |
/ ____ | / ____ |
/ 135 27*\/ 21 | / 135 27*\/ 21 |
2*3 / --- + --------- | 2*3 / --- + --------- |
\/ 2 2 \ \/ 2 2 /
$$x_{1} = \frac{3}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6} + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6}\right)$$
_________________ / _________________ \
/ ____ | / ____ |
/ 135 27*\/ 21 | ___ / 135 27*\/ 21 |
3 / --- + --------- | \/ 3 *3 / --- + --------- ___ |
\/ 2 2 3 | \/ 2 2 3*\/ 3 |
x2 = ---------------------- + ------------------------ + I*|- ---------------------------- + ------------------------|
6 _________________ | 6 _________________|
/ ____ | / ____ |
/ 135 27*\/ 21 | / 135 27*\/ 21 |
2*3 / --- + --------- | 2*3 / --- + --------- |
\/ 2 2 \ \/ 2 2 /
$$x_{2} = \frac{3}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6} + \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}\right)$$
_________________
/ ____
/ 135 27*\/ 21
3 / --- + ---------
3 \/ 2 2
x3 = - ---------------------- - ----------------------
_________________ 3
/ ____
/ 135 27*\/ 21
3 / --- + ---------
\/ 2 2
$$x_{3} = - \frac{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}$$
x3 = -(27*sqrt(21)/2 + 135/2)^(1/3)/3 - 3/(27*sqrt(21)/2 + 135/2)^(1/3)
Suma y producto de raíces
[src]
suma
_________________ / _________________\ _________________ / _________________ \ _________________
/ ____ | / ____ | / ____ | / ____ | / ____
/ 135 27*\/ 21 | ___ / 135 27*\/ 21 | / 135 27*\/ 21 | ___ / 135 27*\/ 21 | / 135 27*\/ 21
3 / --- + --------- | ___ \/ 3 *3 / --- + --------- | 3 / --- + --------- | \/ 3 *3 / --- + --------- ___ | 3 / --- + ---------
\/ 2 2 3 | 3*\/ 3 \/ 2 2 | \/ 2 2 3 | \/ 2 2 3*\/ 3 | 3 \/ 2 2
---------------------- + ------------------------ + I*|- ------------------------ + ----------------------------| + ---------------------- + ------------------------ + I*|- ---------------------------- + ------------------------| + - ---------------------- - ----------------------
6 _________________ | _________________ 6 | 6 _________________ | 6 _________________| _________________ 3
/ ____ | / ____ | / ____ | / ____ | / ____
/ 135 27*\/ 21 | / 135 27*\/ 21 | / 135 27*\/ 21 | / 135 27*\/ 21 | / 135 27*\/ 21
2*3 / --- + --------- | 2*3 / --- + --------- | 2*3 / --- + --------- | 2*3 / --- + --------- | 3 / --- + ---------
\/ 2 2 \ \/ 2 2 / \/ 2 2 \ \/ 2 2 / \/ 2 2
$$\left(- \frac{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}\right) + \left(\left(\frac{3}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6} + \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}\right)\right) + \left(\frac{3}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6} + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6}\right)\right)\right)$$
=
/ _________________\ / _________________ \ | / ____ | | / ____ | | ___ / 135 27*\/ 21 | | ___ / 135 27*\/ 21 | | ___ \/ 3 *3 / --- + --------- | | \/ 3 *3 / --- + --------- ___ | | 3*\/ 3 \/ 2 2 | | \/ 2 2 3*\/ 3 | I*|- ------------------------ + ----------------------------| + I*|- ---------------------------- + ------------------------| | _________________ 6 | | 6 _________________| | / ____ | | / ____ | | / 135 27*\/ 21 | | / 135 27*\/ 21 | | 2*3 / --- + --------- | | 2*3 / --- + --------- | \ \/ 2 2 / \ \/ 2 2 /
$$i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6} + \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}\right) + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6}\right)$$
producto
/ _________________ / _________________\\ / _________________ / _________________ \\ / _________________\ | / ____ | / ____ || | / ____ | / ____ || | / ____ | | / 135 27*\/ 21 | ___ / 135 27*\/ 21 || | / 135 27*\/ 21 | ___ / 135 27*\/ 21 || | / 135 27*\/ 21 | |3 / --- + --------- | ___ \/ 3 *3 / --- + --------- || |3 / --- + --------- | \/ 3 *3 / --- + --------- ___ || | 3 / --- + --------- | |\/ 2 2 3 | 3*\/ 3 \/ 2 2 || |\/ 2 2 3 | \/ 2 2 3*\/ 3 || | 3 \/ 2 2 | |---------------------- + ------------------------ + I*|- ------------------------ + ----------------------------||*|---------------------- + ------------------------ + I*|- ---------------------------- + ------------------------||*|- ---------------------- - ----------------------| | 6 _________________ | _________________ 6 || | 6 _________________ | 6 _________________|| | _________________ 3 | | / ____ | / ____ || | / ____ | / ____ || | / ____ | | / 135 27*\/ 21 | / 135 27*\/ 21 || | / 135 27*\/ 21 | / 135 27*\/ 21 || | / 135 27*\/ 21 | | 2*3 / --- + --------- | 2*3 / --- + --------- || | 2*3 / --- + --------- | 2*3 / --- + --------- || | 3 / --- + --------- | \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 /
$$\left(\frac{3}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6} + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6}\right)\right) \left(\frac{3}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{6} + \frac{3 \sqrt{3}}{2 \sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27 \sqrt{21}}{2} + \frac{135}{2}}}\right)$$
=
-5
$$-5$$
-5
Respuesta numérica
[src]
x1 = 1.1395093930833 + 0.946279541560099*i
x2 = 1.1395093930833 - 0.946279541560099*i
x3 = -2.27901878616659
x3 = -2.27901878616659
Gráfico