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Ecuación 5*x=32+x
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Ecuación 3*x^2+13*x-10=0
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Ecuación (2*x^2+7*x+3)/(x^2-9)=1
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Ecuación 3x=6
- Expresar {x} en función de y en la ecuación:
- -6*x+11*y=-5
- -15*x+7*y=1
- -11*x-11*y=4
- 18*x-14*y=-2
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Expresiones idénticas
- x^ tres - cuatro *x^ dos +9x+ treinta y seis = cero
- x al cubo menos 4 multiplicar por x al cuadrado más 9x más 36 es igual a 0
- x en el grado tres menos cuatro multiplicar por x en el grado dos más 9x más treinta y seis es igual a cero
- x3-4*x2+9x+36=0
- x³-4*x²+9x+36=0
- x en el grado 3-4*x en el grado 2+9x+36=0
- x^3-4x^2+9x+36=0
- x3-4x2+9x+36=0
- x^3-4*x^2+9x+36=O
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Expresiones semejantes
- x^3-4*x^2+9x-36=0
- x^3+4*x^2+9x+36=0
- x^3-4*x^2-9x+36=0
x^3-4*x^2+9x+36=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 x - 4*x + 9*x + 36 = 0
$$\left(9 x + \left(x^{3} - 4 x^{2}\right)\right) + 36 = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = 9$$
$$v = \frac{d}{a}$$
$$v = 36$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 4$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 9$$
$$x_{1} x_{2} x_{3} = 36$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = 9$$
$$v = \frac{d}{a}$$
$$v = 36$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 4$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 9$$
$$x_{1} x_{2} x_{3} = 36$$
Respuesta rápida
[src]
__________________ / __________________ \
3 / ______ | ___ 3 / ______ ___ |
4 11 \/ 584 + 9*\/ 4227 |\/ 3 *\/ 584 + 9*\/ 4227 11*\/ 3 |
x1 = - - ----------------------- + --------------------- + I*|--------------------------- + -----------------------|
3 __________________ 6 | 6 __________________|
3 / ______ | 3 / ______ |
6*\/ 584 + 9*\/ 4227 \ 6*\/ 584 + 9*\/ 4227 /
$$x_{1} = - \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(\frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6}\right)$$
__________________ / __________________\
3 / ______ | ___ ___ 3 / ______ |
4 11 \/ 584 + 9*\/ 4227 | 11*\/ 3 \/ 3 *\/ 584 + 9*\/ 4227 |
x2 = - - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------|
3 __________________ 6 | __________________ 6 |
3 / ______ | 3 / ______ |
6*\/ 584 + 9*\/ 4227 \ 6*\/ 584 + 9*\/ 4227 /
$$x_{2} = - \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6} - \frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}}\right)$$
__________________
3 / ______
4 \/ 584 + 9*\/ 4227 11
x3 = - - --------------------- + -----------------------
3 3 __________________
3 / ______
3*\/ 584 + 9*\/ 4227
$$x_{3} = - \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{3} + \frac{11}{3 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3}$$
x3 = -(584 + 9*sqrt(4227))^(1/3)/3 + 11/(3*(584 + 9*sqrt(4227))^(1/3)) + 4/3
Suma y producto de raíces
[src]
suma
__________________ / __________________ \ __________________ / __________________\ __________________
3 / ______ | ___ 3 / ______ ___ | 3 / ______ | ___ ___ 3 / ______ | 3 / ______
4 11 \/ 584 + 9*\/ 4227 |\/ 3 *\/ 584 + 9*\/ 4227 11*\/ 3 | 4 11 \/ 584 + 9*\/ 4227 | 11*\/ 3 \/ 3 *\/ 584 + 9*\/ 4227 | 4 \/ 584 + 9*\/ 4227 11
- - ----------------------- + --------------------- + I*|--------------------------- + -----------------------| + - - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------| + - - --------------------- + -----------------------
3 __________________ 6 | 6 __________________| 3 __________________ 6 | __________________ 6 | 3 3 __________________
3 / ______ | 3 / ______ | 3 / ______ | 3 / ______ | 3 / ______
6*\/ 584 + 9*\/ 4227 \ 6*\/ 584 + 9*\/ 4227 / 6*\/ 584 + 9*\/ 4227 \ 6*\/ 584 + 9*\/ 4227 / 3*\/ 584 + 9*\/ 4227
$$\left(- \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{3} + \frac{11}{3 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3}\right) + \left(\left(- \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6} - \frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}}\right)\right) + \left(- \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(\frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6}\right)\right)\right)$$
=
/ __________________\ / __________________ \
| ___ ___ 3 / ______ | | ___ 3 / ______ ___ |
| 11*\/ 3 \/ 3 *\/ 584 + 9*\/ 4227 | |\/ 3 *\/ 584 + 9*\/ 4227 11*\/ 3 |
4 + I*|- ----------------------- - ---------------------------| + I*|--------------------------- + -----------------------|
| __________________ 6 | | 6 __________________|
| 3 / ______ | | 3 / ______ |
\ 6*\/ 584 + 9*\/ 4227 / \ 6*\/ 584 + 9*\/ 4227 /
$$4 + i \left(- \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6} - \frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}}\right) + i \left(\frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6}\right)$$
producto
/ __________________ / __________________ \\ / __________________ / __________________\\ / __________________ \ | 3 / ______ | ___ 3 / ______ ___ || | 3 / ______ | ___ ___ 3 / ______ || | 3 / ______ | |4 11 \/ 584 + 9*\/ 4227 |\/ 3 *\/ 584 + 9*\/ 4227 11*\/ 3 || |4 11 \/ 584 + 9*\/ 4227 | 11*\/ 3 \/ 3 *\/ 584 + 9*\/ 4227 || |4 \/ 584 + 9*\/ 4227 11 | |- - ----------------------- + --------------------- + I*|--------------------------- + -----------------------||*|- - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------||*|- - --------------------- + -----------------------| |3 __________________ 6 | 6 __________________|| |3 __________________ 6 | __________________ 6 || |3 3 __________________| | 3 / ______ | 3 / ______ || | 3 / ______ | 3 / ______ || | 3 / ______ | \ 6*\/ 584 + 9*\/ 4227 \ 6*\/ 584 + 9*\/ 4227 // \ 6*\/ 584 + 9*\/ 4227 \ 6*\/ 584 + 9*\/ 4227 // \ 3*\/ 584 + 9*\/ 4227 /
$$\left(- \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(\frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6}\right)\right) \left(- \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6} - \frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}}\right)\right) \left(- \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{3} + \frac{11}{3 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3}\right)$$
=
-36
$$-36$$
-36
Respuesta numérica
[src]
x1 = -1.83017552053575
x2 = 2.91508776026788 + 3.34253015963173*i
x3 = 2.91508776026788 - 3.34253015963173*i
x3 = 2.91508776026788 - 3.34253015963173*i