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- La ecuación:
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Ecuación 6*x^2+x-7=0
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Ecuación 2-5(3+2x)=17
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Ecuación (6*x+8)/2+5=5*x/3
-
Ecuación 2+3x=−2x−13
- Expresar {x} en función de y en la ecuación:
- 6*x+4*y=15
- -4*x+4*y=-9
- 3*x-12*y=-14
- 1*x+4*y=-16
- Gráfico de la función y =:
-
x^3+2*x-13
-
Expresiones idénticas
- x^ tres + dos *x- trece = cero
- x al cubo más 2 multiplicar por x menos 13 es igual a 0
- x en el grado tres más dos multiplicar por x menos trece es igual a cero
- x3+2*x-13=0
- x³+2*x-13=0
- x en el grado 3+2*x-13=0
- x^3+2x-13=0
- x3+2x-13=0
- x^3+2*x-13=O
-
Expresiones semejantes
- x^3+2*x+13=0
- x^3-2*x-13=0
x^3+2*x-13=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
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2$$
$$v = \frac{d}{a}$$
$$v = -13$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 2$$
$$x_{1} x_{2} x_{3} = -13$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2$$
$$v = \frac{d}{a}$$
$$v = -13$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 2$$
$$x_{1} x_{2} x_{3} = -13$$
Suma y producto de raíces
[src]
suma
________________ / ________________ \ ________________ / ________________ \
/ _______ | / _______ | / _______ | / _______ |
/ 13 \/ 13785 | ___ / 13 \/ 13785 | / 13 \/ 13785 | ___ / 13 \/ 13785 | ________________
3 / -- + --------- | \/ 3 *3 / -- + --------- ___ | 3 / -- + --------- |\/ 3 *3 / -- + --------- ___ | / _______
\/ 2 18 1 | \/ 2 18 \/ 3 | \/ 2 18 1 | \/ 2 18 \/ 3 | / 13 \/ 13785 2
- --------------------- + ----------------------- + I*|- --------------------------- - -----------------------| + - --------------------- + ----------------------- + I*|--------------------------- + -----------------------| + 3 / -- + --------- - -----------------------
2 ________________ | 2 ________________| 2 ________________ | 2 ________________| \/ 2 18 ________________
/ _______ | / _______ | / _______ | / _______ | / _______
/ 13 \/ 13785 | / 13 \/ 13785 | / 13 \/ 13785 | / 13 \/ 13785 | / 13 \/ 13785
3*3 / -- + --------- | 3*3 / -- + --------- | 3*3 / -- + --------- | 3*3 / -- + --------- | 3*3 / -- + ---------
\/ 2 18 \ \/ 2 18 / \/ 2 18 \ \/ 2 18 / \/ 2 18
$$\left(- \frac{2}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2}\right)\right)\right)$$
=
/ ________________ \ / ________________ \ | / _______ | | / _______ | | ___ / 13 \/ 13785 | | ___ / 13 \/ 13785 | |\/ 3 *3 / -- + --------- ___ | | \/ 3 *3 / -- + --------- ___ | | \/ 2 18 \/ 3 | | \/ 2 18 \/ 3 | I*|--------------------------- + -----------------------| + I*|- --------------------------- - -----------------------| | 2 ________________| | 2 ________________| | / _______ | | / _______ | | / 13 \/ 13785 | | / 13 \/ 13785 | | 3*3 / -- + --------- | | 3*3 / -- + --------- | \ \/ 2 18 / \ \/ 2 18 /
$$i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}\right) + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2}\right)$$
producto
/ ________________ / ________________ \\ / ________________ / ________________ \\ | / _______ | / _______ || | / _______ | / _______ || | / 13 \/ 13785 | ___ / 13 \/ 13785 || | / 13 \/ 13785 | ___ / 13 \/ 13785 || / ________________ \ | 3 / -- + --------- | \/ 3 *3 / -- + --------- ___ || | 3 / -- + --------- |\/ 3 *3 / -- + --------- ___ || | / _______ | | \/ 2 18 1 | \/ 2 18 \/ 3 || | \/ 2 18 1 | \/ 2 18 \/ 3 || | / 13 \/ 13785 2 | |- --------------------- + ----------------------- + I*|- --------------------------- - -----------------------||*|- --------------------- + ----------------------- + I*|--------------------------- + -----------------------||*|3 / -- + --------- - -----------------------| | 2 ________________ | 2 ________________|| | 2 ________________ | 2 ________________|| |\/ 2 18 ________________| | / _______ | / _______ || | / _______ | / _______ || | / _______ | | / 13 \/ 13785 | / 13 \/ 13785 || | / 13 \/ 13785 | / 13 \/ 13785 || | / 13 \/ 13785 | | 3*3 / -- + --------- | 3*3 / -- + --------- || | 3*3 / -- + --------- | 3*3 / -- + --------- || | 3*3 / -- + --------- | \ \/ 2 18 \ \/ 2 18 // \ \/ 2 18 \ \/ 2 18 // \ \/ 2 18 /
$$\left(- \frac{\sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}\right)\right) \left(- \frac{2}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}\right)$$
=
13
$$13$$
13
Respuesta rápida
[src]
________________ / ________________ \
/ _______ | / _______ |
/ 13 \/ 13785 | ___ / 13 \/ 13785 |
3 / -- + --------- | \/ 3 *3 / -- + --------- ___ |
\/ 2 18 1 | \/ 2 18 \/ 3 |
x1 = - --------------------- + ----------------------- + I*|- --------------------------- - -----------------------|
2 ________________ | 2 ________________|
/ _______ | / _______ |
/ 13 \/ 13785 | / 13 \/ 13785 |
3*3 / -- + --------- | 3*3 / -- + --------- |
\/ 2 18 \ \/ 2 18 /
$$x_{1} = - \frac{\sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}\right)$$
________________ / ________________ \
/ _______ | / _______ |
/ 13 \/ 13785 | ___ / 13 \/ 13785 |
3 / -- + --------- |\/ 3 *3 / -- + --------- ___ |
\/ 2 18 1 | \/ 2 18 \/ 3 |
x2 = - --------------------- + ----------------------- + I*|--------------------------- + -----------------------|
2 ________________ | 2 ________________|
/ _______ | / _______ |
/ 13 \/ 13785 | / 13 \/ 13785 |
3*3 / -- + --------- | 3*3 / -- + --------- |
\/ 2 18 \ \/ 2 18 /
$$x_{2} = - \frac{\sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}}{2}\right)$$
________________
/ _______
/ 13 \/ 13785 2
x3 = 3 / -- + --------- - -----------------------
\/ 2 18 ________________
/ _______
/ 13 \/ 13785
3*3 / -- + ---------
\/ 2 18
$$x_{3} = - \frac{2}{3 \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}} + \sqrt[3]{\frac{13}{2} + \frac{\sqrt{13785}}{18}}$$
x3 = -2/(3*(13/2 + sqrt(13785)/18)^(1/3)) + (13/2 + sqrt(13785)/18)^(1/3)
Respuesta numérica
[src]
x1 = -1.03467196669583 - 2.28290127600793*i
x2 = -1.03467196669583 + 2.28290127600793*i
x3 = 2.06934393339166
x3 = 2.06934393339166
Gráfico