Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x^2+5x=36
-
Ecuación 3*x-6=x+4
-
Ecuación 9^x-8*3^x-9=0
-
Ecuación 1-8*x/15=4*x/9
- Expresar {x} en función de y en la ecuación:
- 10*x-15*y=16
- -17*x+2*y=-4
- -2*x-19*y=3
- 6*x+17*y=-11
-
Expresiones idénticas
- x^ tres - tres *x^ dos - cuatro *x- doce = cero
- x al cubo menos 3 multiplicar por x al cuadrado menos 4 multiplicar por x menos 12 es igual a 0
- x en el grado tres menos tres multiplicar por x en el grado dos menos cuatro multiplicar por x menos doce es igual a cero
- x3-3*x2-4*x-12=0
- x³-3*x²-4*x-12=0
- x en el grado 3-3*x en el grado 2-4*x-12=0
- x^3-3x^2-4x-12=0
- x3-3x2-4x-12=0
- x^3-3*x^2-4*x-12=O
-
Expresiones semejantes
- x^3+3*x^2-4*x-12=0
- x^3-3*x^2-4*x+12=0
- x^3-3*x^2+4*x-12=0
x^3-3*x^2-4*x-12=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 x - 3*x - 4*x - 12 = 0
$$\left(- 4 x + \left(x^{3} - 3 x^{2}\right)\right) - 12 = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = -4$$
$$v = \frac{d}{a}$$
$$v = -12$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 3$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -4$$
$$x_{1} x_{2} x_{3} = -12$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = -4$$
$$v = \frac{d}{a}$$
$$v = -12$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 3$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -4$$
$$x_{1} x_{2} x_{3} = -12$$
Respuesta rápida
[src]
________________ / ________________ \
/ ______ | / ______ |
/ 2*\/ 1383 | ___ / 2*\/ 1383 |
3 / 9 + ---------- | \/ 3 *3 / 9 + ---------- ___ |
7 \/ 9 | \/ 9 7*\/ 3 |
x1 = 1 - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------|
________________ 2 | 2 ________________|
/ ______ | / ______ |
/ 2*\/ 1383 | / 2*\/ 1383 |
6*3 / 9 + ---------- | 6*3 / 9 + ---------- |
\/ 9 \ \/ 9 /
$$x_{1} = - \frac{\sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} - \frac{7}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} + \frac{7 \sqrt{3}}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}\right)$$
________________ / ________________ \
/ ______ | / ______ |
/ 2*\/ 1383 | ___ / 2*\/ 1383 |
3 / 9 + ---------- |\/ 3 *3 / 9 + ---------- ___ |
7 \/ 9 | \/ 9 7*\/ 3 |
x2 = 1 - ----------------------- - --------------------- + I*|--------------------------- - -----------------------|
________________ 2 | 2 ________________|
/ ______ | / ______ |
/ 2*\/ 1383 | / 2*\/ 1383 |
6*3 / 9 + ---------- | 6*3 / 9 + ---------- |
\/ 9 \ \/ 9 /
$$x_{2} = - \frac{\sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} - \frac{7}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1 + i \left(- \frac{7 \sqrt{3}}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2}\right)$$
________________
/ ______
/ 2*\/ 1383 7
x3 = 1 + 3 / 9 + ---------- + -----------------------
\/ 9 ________________
/ ______
/ 2*\/ 1383
3*3 / 9 + ----------
\/ 9
$$x_{3} = \frac{7}{3 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1 + \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}$$
x3 = 7/(3*(2*sqrt(1383)/9 + 9)^(1/3)) + 1 + (2*sqrt(1383)/9 + 9)^(1/3)
Suma y producto de raíces
[src]
suma
________________ / ________________ \ ________________ / ________________ \
/ ______ | / ______ | / ______ | / ______ |
/ 2*\/ 1383 | ___ / 2*\/ 1383 | / 2*\/ 1383 | ___ / 2*\/ 1383 | ________________
3 / 9 + ---------- | \/ 3 *3 / 9 + ---------- ___ | 3 / 9 + ---------- |\/ 3 *3 / 9 + ---------- ___ | / ______
7 \/ 9 | \/ 9 7*\/ 3 | 7 \/ 9 | \/ 9 7*\/ 3 | / 2*\/ 1383 7
1 - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------| + 1 - ----------------------- - --------------------- + I*|--------------------------- - -----------------------| + 1 + 3 / 9 + ---------- + -----------------------
________________ 2 | 2 ________________| ________________ 2 | 2 ________________| \/ 9 ________________
/ ______ | / ______ | / ______ | / ______ | / ______
/ 2*\/ 1383 | / 2*\/ 1383 | / 2*\/ 1383 | / 2*\/ 1383 | / 2*\/ 1383
6*3 / 9 + ---------- | 6*3 / 9 + ---------- | 6*3 / 9 + ---------- | 6*3 / 9 + ---------- | 3*3 / 9 + ----------
\/ 9 \ \/ 9 / \/ 9 \ \/ 9 / \/ 9
$$\left(\frac{7}{3 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1 + \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}\right) + \left(\left(- \frac{\sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} - \frac{7}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} + \frac{7 \sqrt{3}}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} - \frac{7}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1 + i \left(- \frac{7 \sqrt{3}}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2}\right)\right)\right)$$
=
/ ________________ \ / ________________ \
| / ______ | | / ______ |
| ___ / 2*\/ 1383 | | ___ / 2*\/ 1383 |
|\/ 3 *3 / 9 + ---------- ___ | | \/ 3 *3 / 9 + ---------- ___ |
| \/ 9 7*\/ 3 | | \/ 9 7*\/ 3 |
3 + I*|--------------------------- - -----------------------| + I*|- --------------------------- + -----------------------|
| 2 ________________| | 2 ________________|
| / ______ | | / ______ |
| / 2*\/ 1383 | | / 2*\/ 1383 |
| 6*3 / 9 + ---------- | | 6*3 / 9 + ---------- |
\ \/ 9 / \ \/ 9 /
$$3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} + \frac{7 \sqrt{3}}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}\right) + i \left(- \frac{7 \sqrt{3}}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2}\right)$$
producto
/ ________________ / ________________ \\ / ________________ / ________________ \\ | / ______ | / ______ || | / ______ | / ______ || | / 2*\/ 1383 | ___ / 2*\/ 1383 || | / 2*\/ 1383 | ___ / 2*\/ 1383 || / ________________ \ | 3 / 9 + ---------- | \/ 3 *3 / 9 + ---------- ___ || | 3 / 9 + ---------- |\/ 3 *3 / 9 + ---------- ___ || | / ______ | | 7 \/ 9 | \/ 9 7*\/ 3 || | 7 \/ 9 | \/ 9 7*\/ 3 || | / 2*\/ 1383 7 | |1 - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------||*|1 - ----------------------- - --------------------- + I*|--------------------------- - -----------------------||*|1 + 3 / 9 + ---------- + -----------------------| | ________________ 2 | 2 ________________|| | ________________ 2 | 2 ________________|| | \/ 9 ________________| | / ______ | / ______ || | / ______ | / ______ || | / ______ | | / 2*\/ 1383 | / 2*\/ 1383 || | / 2*\/ 1383 | / 2*\/ 1383 || | / 2*\/ 1383 | | 6*3 / 9 + ---------- | 6*3 / 9 + ---------- || | 6*3 / 9 + ---------- | 6*3 / 9 + ---------- || | 3*3 / 9 + ---------- | \ \/ 9 \ \/ 9 // \ \/ 9 \ \/ 9 // \ \/ 9 /
$$\left(- \frac{\sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} - \frac{7}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1 + i \left(- \frac{7 \sqrt{3}}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} - \frac{7}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} + \frac{7 \sqrt{3}}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}\right)\right) \left(\frac{7}{3 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1 + \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}\right)$$
=
12
$$12$$
12
Respuesta numérica
[src]
x1 = 4.48733844445223
x2 = -0.743669222226114 + 1.45641582991118*i
x3 = -0.743669222226114 - 1.45641582991118*i
x3 = -0.743669222226114 - 1.45641582991118*i
Gráfico