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- La ecuación:
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Ecuación x+9=0
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Ecuación 2x^2+7x-9=0
-
Ecuación 5*x^2+9*x=0
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Ecuación 3x^2=2x+x^3
- Expresar {x} en función de y en la ecuación:
- -6*x+11*y=-5
- -15*x+7*y=1
- -14*x+4*y=-16
- 11*x-9*y=-4
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Expresiones idénticas
- x^ tres + dos *x^ dos -5x+ nueve = cero
- x al cubo más 2 multiplicar por x al cuadrado menos 5x más 9 es igual a 0
- x en el grado tres más dos multiplicar por x en el grado dos menos 5x más nueve es igual a cero
- x3+2*x2-5x+9=0
- x³+2*x²-5x+9=0
- x en el grado 3+2*x en el grado 2-5x+9=0
- x^3+2x^2-5x+9=0
- x3+2x2-5x+9=0
- x^3+2*x^2-5x+9=O
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Expresiones semejantes
- x^3+2*x^2+5x+9=0
- x^3+2*x^2-5x-9=0
- x^3-2*x^2-5x+9=0
x^3+2*x^2-5x+9=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 x + 2*x - 5*x + 9 = 0
$$\left(- 5 x + \left(x^{3} + 2 x^{2}\right)\right) + 9 = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -5$$
$$v = \frac{d}{a}$$
$$v = 9$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -2$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -5$$
$$x_{1} x_{2} x_{3} = 9$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -5$$
$$v = \frac{d}{a}$$
$$v = 9$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -2$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -5$$
$$x_{1} x_{2} x_{3} = 9$$
Respuesta rápida
[src]
__________________ / __________________\
/ ______ | / ______ |
/ 349 9*\/ 1165 | ___ / 349 9*\/ 1165 |
3 / --- + ---------- | ___ \/ 3 *3 / --- + ---------- |
2 \/ 2 2 19 | 19*\/ 3 \/ 2 2 |
x1 = - - + ----------------------- + ------------------------- + I*|- ------------------------- + -----------------------------|
3 6 __________________ | __________________ 6 |
/ ______ | / ______ |
/ 349 9*\/ 1165 | / 349 9*\/ 1165 |
6*3 / --- + ---------- | 6*3 / --- + ---------- |
\/ 2 2 \ \/ 2 2 /
$$x_{1} = - \frac{2}{3} + \frac{19}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} + \frac{\sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6} + i \left(- \frac{19 \sqrt{3}}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6}\right)$$
__________________ / __________________ \
/ ______ | / ______ |
/ 349 9*\/ 1165 | ___ / 349 9*\/ 1165 |
3 / --- + ---------- | \/ 3 *3 / --- + ---------- ___ |
2 \/ 2 2 19 | \/ 2 2 19*\/ 3 |
x2 = - - + ----------------------- + ------------------------- + I*|- ----------------------------- + -------------------------|
3 6 __________________ | 6 __________________|
/ ______ | / ______ |
/ 349 9*\/ 1165 | / 349 9*\/ 1165 |
6*3 / --- + ---------- | 6*3 / --- + ---------- |
\/ 2 2 \ \/ 2 2 /
$$x_{2} = - \frac{2}{3} + \frac{19}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} + \frac{\sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6} + \frac{19 \sqrt{3}}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}\right)$$
__________________
/ ______
/ 349 9*\/ 1165
3 / --- + ----------
2 19 \/ 2 2
x3 = - - - ------------------------- - -----------------------
3 __________________ 3
/ ______
/ 349 9*\/ 1165
3*3 / --- + ----------
\/ 2 2
$$x_{3} = - \frac{\sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{3} - \frac{19}{3 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} - \frac{2}{3}$$
x3 = -(9*sqrt(1165)/2 + 349/2)^(1/3)/3 - 19/(3*(9*sqrt(1165)/2 + 349/2)^(1/3)) - 2/3
Suma y producto de raíces
[src]
suma
__________________ / __________________\ __________________ / __________________ \ __________________
/ ______ | / ______ | / ______ | / ______ | / ______
/ 349 9*\/ 1165 | ___ / 349 9*\/ 1165 | / 349 9*\/ 1165 | ___ / 349 9*\/ 1165 | / 349 9*\/ 1165
3 / --- + ---------- | ___ \/ 3 *3 / --- + ---------- | 3 / --- + ---------- | \/ 3 *3 / --- + ---------- ___ | 3 / --- + ----------
2 \/ 2 2 19 | 19*\/ 3 \/ 2 2 | 2 \/ 2 2 19 | \/ 2 2 19*\/ 3 | 2 19 \/ 2 2
- - + ----------------------- + ------------------------- + I*|- ------------------------- + -----------------------------| + - - + ----------------------- + ------------------------- + I*|- ----------------------------- + -------------------------| + - - - ------------------------- - -----------------------
3 6 __________________ | __________________ 6 | 3 6 __________________ | 6 __________________| 3 __________________ 3
/ ______ | / ______ | / ______ | / ______ | / ______
/ 349 9*\/ 1165 | / 349 9*\/ 1165 | / 349 9*\/ 1165 | / 349 9*\/ 1165 | / 349 9*\/ 1165
6*3 / --- + ---------- | 6*3 / --- + ---------- | 6*3 / --- + ---------- | 6*3 / --- + ---------- | 3*3 / --- + ----------
\/ 2 2 \ \/ 2 2 / \/ 2 2 \ \/ 2 2 / \/ 2 2
$$\left(- \frac{\sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{3} - \frac{19}{3 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} - \frac{2}{3}\right) + \left(\left(- \frac{2}{3} + \frac{19}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} + \frac{\sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6} + \frac{19 \sqrt{3}}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}\right)\right) + \left(- \frac{2}{3} + \frac{19}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} + \frac{\sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6} + i \left(- \frac{19 \sqrt{3}}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6}\right)\right)\right)$$
=
/ __________________\ / __________________ \
| / ______ | | / ______ |
| ___ / 349 9*\/ 1165 | | ___ / 349 9*\/ 1165 |
| ___ \/ 3 *3 / --- + ---------- | | \/ 3 *3 / --- + ---------- ___ |
| 19*\/ 3 \/ 2 2 | | \/ 2 2 19*\/ 3 |
-2 + I*|- ------------------------- + -----------------------------| + I*|- ----------------------------- + -------------------------|
| __________________ 6 | | 6 __________________|
| / ______ | | / ______ |
| / 349 9*\/ 1165 | | / 349 9*\/ 1165 |
| 6*3 / --- + ---------- | | 6*3 / --- + ---------- |
\ \/ 2 2 / \ \/ 2 2 /
$$-2 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6} + \frac{19 \sqrt{3}}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}\right) + i \left(- \frac{19 \sqrt{3}}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6}\right)$$
producto
/ __________________ / __________________\\ / __________________ / __________________ \\ / __________________\ | / ______ | / ______ || | / ______ | / ______ || | / ______ | | / 349 9*\/ 1165 | ___ / 349 9*\/ 1165 || | / 349 9*\/ 1165 | ___ / 349 9*\/ 1165 || | / 349 9*\/ 1165 | | 3 / --- + ---------- | ___ \/ 3 *3 / --- + ---------- || | 3 / --- + ---------- | \/ 3 *3 / --- + ---------- ___ || | 3 / --- + ---------- | | 2 \/ 2 2 19 | 19*\/ 3 \/ 2 2 || | 2 \/ 2 2 19 | \/ 2 2 19*\/ 3 || | 2 19 \/ 2 2 | |- - + ----------------------- + ------------------------- + I*|- ------------------------- + -----------------------------||*|- - + ----------------------- + ------------------------- + I*|- ----------------------------- + -------------------------||*|- - - ------------------------- - -----------------------| | 3 6 __________________ | __________________ 6 || | 3 6 __________________ | 6 __________________|| | 3 __________________ 3 | | / ______ | / ______ || | / ______ | / ______ || | / ______ | | / 349 9*\/ 1165 | / 349 9*\/ 1165 || | / 349 9*\/ 1165 | / 349 9*\/ 1165 || | / 349 9*\/ 1165 | | 6*3 / --- + ---------- | 6*3 / --- + ---------- || | 6*3 / --- + ---------- | 6*3 / --- + ---------- || | 3*3 / --- + ---------- | \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 /
$$\left(- \frac{2}{3} + \frac{19}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} + \frac{\sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6} + i \left(- \frac{19 \sqrt{3}}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6}\right)\right) \left(- \frac{2}{3} + \frac{19}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} + \frac{\sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{6} + \frac{19 \sqrt{3}}{6 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}}{3} - \frac{19}{3 \sqrt[3]{\frac{9 \sqrt{1165}}{2} + \frac{349}{2}}} - \frac{2}{3}\right)$$
=
-9
$$-9$$
-9
Respuesta numérica
[src]
x1 = 0.941979791567692 + 1.19578298592868*i
x2 = -3.88395958313538
x3 = 0.941979791567692 - 1.19578298592868*i
x3 = 0.941979791567692 - 1.19578298592868*i