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- La ecuación:
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Ecuación 3*x^2-x+2=0
-
Ecuación 1-x/2=x/3
-
Ecuación 3*x^2-9=0
-
Ecuación 0,084:(6,2-x)=1,2
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- -17*x+2*y=9
- 10*x-15*y=16
- Límite de la función:
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x^3
- Derivada de:
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x^3
- Gráfico de la función y =:
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x^3
- x^2+7*x+7
- Descomponer al cuadrado:
- x^2+7*x+7
-
Expresiones idénticas
- x^ tres =x^ dos + siete *x+ siete
- x al cubo es igual a x al cuadrado más 7 multiplicar por x más 7
- x en el grado tres es igual a x en el grado dos más siete multiplicar por x más siete
- x3=x2+7*x+7
- x³=x²+7*x+7
- x en el grado 3=x en el grado 2+7*x+7
- x^3=x^2+7x+7
- x3=x2+7x+7
-
Expresiones semejantes
- x^3=x^2-7*x+7
- x^3=x^2+7*x-7
x^3=x^2+7*x+7 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
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -7$$
$$v = \frac{d}{a}$$
$$v = -7$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 1$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -7$$
$$x_{1} x_{2} x_{3} = -7$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -7$$
$$v = \frac{d}{a}$$
$$v = -7$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 1$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -7$$
$$x_{1} x_{2} x_{3} = -7$$
Respuesta rápida
[src]
_______________ / _______________ \
/ _____ | / _____ |
/ 127 \/ 609 | ___ / 127 \/ 609 |
3 / --- + ------- | \/ 3 *3 / --- + ------- ___ |
1 11 \/ 27 9 | \/ 27 9 11*\/ 3 |
x1 = - - ---------------------- - -------------------- + I*|- -------------------------- + ----------------------|
3 _______________ 2 | 2 _______________|
/ _____ | / _____ |
/ 127 \/ 609 | / 127 \/ 609 |
9*3 / --- + ------- | 9*3 / --- + ------- |
\/ 27 9 \ \/ 27 9 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2} - \frac{11}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2} + \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}\right)$$
_______________ / _______________ \
/ _____ | / _____ |
/ 127 \/ 609 | ___ / 127 \/ 609 |
3 / --- + ------- |\/ 3 *3 / --- + ------- ___ |
1 11 \/ 27 9 | \/ 27 9 11*\/ 3 |
x2 = - - ---------------------- - -------------------- + I*|-------------------------- - ----------------------|
3 _______________ 2 | 2 _______________|
/ _____ | / _____ |
/ 127 \/ 609 | / 127 \/ 609 |
9*3 / --- + ------- | 9*3 / --- + ------- |
\/ 27 9 \ \/ 27 9 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2} - \frac{11}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \frac{1}{3} + i \left(- \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2}\right)$$
_______________
/ _____
1 / 127 \/ 609 22
x3 = - + 3 / --- + ------- + ----------------------
3 \/ 27 9 _______________
/ _____
/ 127 \/ 609
9*3 / --- + -------
\/ 27 9
$$x_{3} = \frac{1}{3} + \frac{22}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}$$
x3 = 1/3 + 22/(9*(sqrt(609)/9 + 127/27)^(1/3)) + (sqrt(609)/9 + 127/27)^(1/3)
Suma y producto de raíces
[src]
suma
_______________ / _______________ \ _______________ / _______________ \
/ _____ | / _____ | / _____ | / _____ |
/ 127 \/ 609 | ___ / 127 \/ 609 | / 127 \/ 609 | ___ / 127 \/ 609 | _______________
3 / --- + ------- | \/ 3 *3 / --- + ------- ___ | 3 / --- + ------- |\/ 3 *3 / --- + ------- ___ | / _____
1 11 \/ 27 9 | \/ 27 9 11*\/ 3 | 1 11 \/ 27 9 | \/ 27 9 11*\/ 3 | 1 / 127 \/ 609 22
- - ---------------------- - -------------------- + I*|- -------------------------- + ----------------------| + - - ---------------------- - -------------------- + I*|-------------------------- - ----------------------| + - + 3 / --- + ------- + ----------------------
3 _______________ 2 | 2 _______________| 3 _______________ 2 | 2 _______________| 3 \/ 27 9 _______________
/ _____ | / _____ | / _____ | / _____ | / _____
/ 127 \/ 609 | / 127 \/ 609 | / 127 \/ 609 | / 127 \/ 609 | / 127 \/ 609
9*3 / --- + ------- | 9*3 / --- + ------- | 9*3 / --- + ------- | 9*3 / --- + ------- | 9*3 / --- + -------
\/ 27 9 \ \/ 27 9 / \/ 27 9 \ \/ 27 9 / \/ 27 9
$$\left(\frac{1}{3} + \frac{22}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2} - \frac{11}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2} + \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2} - \frac{11}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \frac{1}{3} + i \left(- \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2}\right)\right)\right)$$
=
/ _______________ \ / _______________ \
| / _____ | | / _____ |
| ___ / 127 \/ 609 | | ___ / 127 \/ 609 |
|\/ 3 *3 / --- + ------- ___ | | \/ 3 *3 / --- + ------- ___ |
| \/ 27 9 11*\/ 3 | | \/ 27 9 11*\/ 3 |
1 + I*|-------------------------- - ----------------------| + I*|- -------------------------- + ----------------------|
| 2 _______________| | 2 _______________|
| / _____ | | / _____ |
| / 127 \/ 609 | | / 127 \/ 609 |
| 9*3 / --- + ------- | | 9*3 / --- + ------- |
\ \/ 27 9 / \ \/ 27 9 /
$$1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2} + \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}\right) + i \left(- \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2}\right)$$
producto
/ _______________ / _______________ \\ / _______________ / _______________ \\ | / _____ | / _____ || | / _____ | / _____ || | / 127 \/ 609 | ___ / 127 \/ 609 || | / 127 \/ 609 | ___ / 127 \/ 609 || / _______________ \ | 3 / --- + ------- | \/ 3 *3 / --- + ------- ___ || | 3 / --- + ------- |\/ 3 *3 / --- + ------- ___ || | / _____ | |1 11 \/ 27 9 | \/ 27 9 11*\/ 3 || |1 11 \/ 27 9 | \/ 27 9 11*\/ 3 || |1 / 127 \/ 609 22 | |- - ---------------------- - -------------------- + I*|- -------------------------- + ----------------------||*|- - ---------------------- - -------------------- + I*|-------------------------- - ----------------------||*|- + 3 / --- + ------- + ----------------------| |3 _______________ 2 | 2 _______________|| |3 _______________ 2 | 2 _______________|| |3 \/ 27 9 _______________| | / _____ | / _____ || | / _____ | / _____ || | / _____ | | / 127 \/ 609 | / 127 \/ 609 || | / 127 \/ 609 | / 127 \/ 609 || | / 127 \/ 609 | | 9*3 / --- + ------- | 9*3 / --- + ------- || | 9*3 / --- + ------- | 9*3 / --- + ------- || | 9*3 / --- + ------- | \ \/ 27 9 \ \/ 27 9 // \ \/ 27 9 \ \/ 27 9 // \ \/ 27 9 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2} - \frac{11}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \frac{1}{3} + i \left(- \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2} - \frac{11}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}{2} + \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}}\right)\right) \left(\frac{1}{3} + \frac{22}{9 \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}} + \sqrt[3]{\frac{\sqrt{609}}{9} + \frac{127}{27}}\right)$$
=
7
$$7$$
7
Respuesta numérica
[src]
x1 = -1.26893029024142 - 0.606970201047238*i
x2 = 3.53786058048283
x3 = -1.26893029024142 + 0.606970201047238*i
x3 = -1.26893029024142 + 0.606970201047238*i