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- La ecuación:
- Ecuación 2*x^2-7*x+12=0
- Ecuación 6(x-9)=x+5
- Ecuación n^2-3n-108=0
- Ecuación x^3+3*x=1
- Expresar {x} en función de y en la ecuación:
- 9*x+7*y=4
- -1*x+7*y=-11
- 1*x+5*y=16
- 9*x-10*y=-3
- Derivada de:
-
x^3+3*x
- Gráfico de la función y =:
-
x^3+3*x
- Límite de la función:
- x^3+3*x
-
Expresiones idénticas
- x^ tres + tres *x= uno
- x al cubo más 3 multiplicar por x es igual a 1
- x en el grado tres más tres multiplicar por x es igual a uno
- x3+3*x=1
- x³+3*x=1
- x en el grado 3+3*x=1
- x^3+3x=1
- x3+3x=1
-
Expresiones semejantes
- x^3-3*x=1
x^3+3*x=1 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
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 3$$
$$v = \frac{d}{a}$$
$$v = -1$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 3$$
$$x_{1} x_{2} x_{3} = -1$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 3$$
$$v = \frac{d}{a}$$
$$v = -1$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 3$$
$$x_{1} x_{2} x_{3} = -1$$
Respuesta rápida
[src]
___________ / ___________\
/ ___ | / ___ |
/ 1 \/ 5 | ___ / 1 \/ 5 |
3 / - + ----- | ___ \/ 3 *3 / - + ----- |
1 \/ 2 2 | \/ 3 \/ 2 2 |
x1 = ------------------ - ---------------- + I*|- ------------------ - ----------------------|
___________ 2 | ___________ 2 |
/ ___ | / ___ |
/ 1 \/ 5 | / 1 \/ 5 |
2*3 / - + ----- | 2*3 / - + ----- |
\/ 2 2 \ \/ 2 2 /
$$x_{1} = - \frac{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2} + \frac{1}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}\right)$$
___________ / ___________\
/ ___ | / ___ |
/ 1 \/ 5 | ___ / 1 \/ 5 |
3 / - + ----- | ___ \/ 3 *3 / - + ----- |
1 \/ 2 2 | \/ 3 \/ 2 2 |
x2 = ------------------ - ---------------- + I*|------------------ + ----------------------|
___________ 2 | ___________ 2 |
/ ___ | / ___ |
/ 1 \/ 5 | / 1 \/ 5 |
2*3 / - + ----- |2*3 / - + ----- |
\/ 2 2 \ \/ 2 2 /
$$x_{2} = - \frac{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2} + \frac{1}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2}\right)$$
___________
/ ___
/ 1 \/ 5 1
x3 = 3 / - + ----- - ----------------
\/ 2 2 ___________
/ ___
/ 1 \/ 5
3 / - + -----
\/ 2 2
$$x_{3} = - \frac{1}{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}$$
x3 = -1/(1/2 + sqrt(5)/2)^(1/3) + (1/2 + sqrt(5)/2)^(1/3)
Suma y producto de raíces
[src]
suma
___________ / ___________\ ___________ / ___________\
/ ___ | / ___ | / ___ | / ___ |
/ 1 \/ 5 | ___ / 1 \/ 5 | / 1 \/ 5 | ___ / 1 \/ 5 | ___________
3 / - + ----- | ___ \/ 3 *3 / - + ----- | 3 / - + ----- | ___ \/ 3 *3 / - + ----- | / ___
1 \/ 2 2 | \/ 3 \/ 2 2 | 1 \/ 2 2 | \/ 3 \/ 2 2 | / 1 \/ 5 1
------------------ - ---------------- + I*|- ------------------ - ----------------------| + ------------------ - ---------------- + I*|------------------ + ----------------------| + 3 / - + ----- - ----------------
___________ 2 | ___________ 2 | ___________ 2 | ___________ 2 | \/ 2 2 ___________
/ ___ | / ___ | / ___ | / ___ | / ___
/ 1 \/ 5 | / 1 \/ 5 | / 1 \/ 5 | / 1 \/ 5 | / 1 \/ 5
2*3 / - + ----- | 2*3 / - + ----- | 2*3 / - + ----- |2*3 / - + ----- | 3 / - + -----
\/ 2 2 \ \/ 2 2 / \/ 2 2 \ \/ 2 2 / \/ 2 2
$$\left(- \frac{1}{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2} + \frac{1}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2} + \frac{1}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2}\right)\right)\right)$$
=
/ ___________\ / ___________\ | / ___ | | / ___ | | ___ / 1 \/ 5 | | ___ / 1 \/ 5 | | ___ \/ 3 *3 / - + ----- | | ___ \/ 3 *3 / - + ----- | | \/ 3 \/ 2 2 | | \/ 3 \/ 2 2 | I*|------------------ + ----------------------| + I*|- ------------------ - ----------------------| | ___________ 2 | | ___________ 2 | | / ___ | | / ___ | | / 1 \/ 5 | | / 1 \/ 5 | |2*3 / - + ----- | | 2*3 / - + ----- | \ \/ 2 2 / \ \/ 2 2 /
$$i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}\right) + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2}\right)$$
producto
/ ___________ / ___________\\ / ___________ / ___________\\ | / ___ | / ___ || | / ___ | / ___ || | / 1 \/ 5 | ___ / 1 \/ 5 || | / 1 \/ 5 | ___ / 1 \/ 5 || / ___________ \ | 3 / - + ----- | ___ \/ 3 *3 / - + ----- || | 3 / - + ----- | ___ \/ 3 *3 / - + ----- || | / ___ | | 1 \/ 2 2 | \/ 3 \/ 2 2 || | 1 \/ 2 2 | \/ 3 \/ 2 2 || | / 1 \/ 5 1 | |------------------ - ---------------- + I*|- ------------------ - ----------------------||*|------------------ - ---------------- + I*|------------------ + ----------------------||*|3 / - + ----- - ----------------| | ___________ 2 | ___________ 2 || | ___________ 2 | ___________ 2 || |\/ 2 2 ___________| | / ___ | / ___ || | / ___ | / ___ || | / ___ | | / 1 \/ 5 | / 1 \/ 5 || | / 1 \/ 5 | / 1 \/ 5 || | / 1 \/ 5 | |2*3 / - + ----- | 2*3 / - + ----- || |2*3 / - + ----- |2*3 / - + ----- || | 3 / - + ----- | \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 /
$$\left(- \frac{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2} + \frac{1}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2} + \frac{1}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}{2} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}}\right)\right) \left(- \frac{1}{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}} + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{5}}{2}}\right)$$
=
1
$$1$$
1
Respuesta numérica
[src]
x1 = -0.161092677313043 - 1.75438095978372*i
x2 = -0.161092677313043 + 1.75438095978372*i
x3 = 0.322185354626086
x3 = 0.322185354626086