Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 2x^2-8=0
-
Ecuación x^4+x^3+x^2+x+1=0
-
Ecuación 2^x=-4
-
Ecuación 15/x=3
- Expresar {x} en función de y en la ecuación:
- 14*x+17*y=19
- -14*x+19*y=-3
- -12*x-11*y=19
- 13*x-11*y=16
-
Expresiones idénticas
- tres *x^ tres + cinco *x^ dos - siete *x+ cinco = cero
- 3 multiplicar por x al cubo más 5 multiplicar por x al cuadrado menos 7 multiplicar por x más 5 es igual a 0
- tres multiplicar por x en el grado tres más cinco multiplicar por x en el grado dos menos siete multiplicar por x más cinco es igual a cero
- 3*x3+5*x2-7*x+5=0
- 3*x³+5*x²-7*x+5=0
- 3*x en el grado 3+5*x en el grado 2-7*x+5=0
- 3x^3+5x^2-7x+5=0
- 3x3+5x2-7x+5=0
- 3*x^3+5*x^2-7*x+5=O
-
Expresiones semejantes
- 3*x^3+5*x^2+7*x+5=0
- 3*x^3+5*x^2-7*x-5=0
- 3*x^3-5*x^2-7*x+5=0
3*x^3+5*x^2-7*x+5=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 3*x + 5*x - 7*x + 5 = 0
$$\left(- 7 x + \left(3 x^{3} + 5 x^{2}\right)\right) + 5 = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(- 7 x + \left(3 x^{3} + 5 x^{2}\right)\right) + 5 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{5 x^{2}}{3} - \frac{7 x}{3} + \frac{5}{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{5}{3}$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{3}$$
$$v = \frac{d}{a}$$
$$v = \frac{5}{3}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{5}{3}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{7}{3}$$
$$x_{1} x_{2} x_{3} = \frac{5}{3}$$
$$\left(- 7 x + \left(3 x^{3} + 5 x^{2}\right)\right) + 5 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{5 x^{2}}{3} - \frac{7 x}{3} + \frac{5}{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{5}{3}$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{3}$$
$$v = \frac{d}{a}$$
$$v = \frac{5}{3}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{5}{3}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{7}{3}$$
$$x_{1} x_{2} x_{3} = \frac{5}{3}$$
Respuesta rápida
[src]
_________________ / _________________\
/ 1205 ______ | ___ / 1205 ______ |
3 / ---- + \/ 1057 | ___ \/ 3 *3 / ---- + \/ 1057 |
5 \/ 27 44 | 44*\/ 3 \/ 27 |
x1 = - - + --------------------- + ------------------------ + I*|- ------------------------ + ---------------------------|
9 6 _________________ | _________________ 6 |
/ 1205 ______ | / 1205 ______ |
27*3 / ---- + \/ 1057 | 27*3 / ---- + \/ 1057 |
\/ 27 \ \/ 27 /
$$x_{1} = - \frac{5}{9} + \frac{44}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} + \frac{\sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6} + i \left(- \frac{44 \sqrt{3}}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} + \frac{\sqrt{3} \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6}\right)$$
_________________ / _________________ \
/ 1205 ______ | ___ / 1205 ______ |
3 / ---- + \/ 1057 | \/ 3 *3 / ---- + \/ 1057 ___ |
5 \/ 27 44 | \/ 27 44*\/ 3 |
x2 = - - + --------------------- + ------------------------ + I*|- --------------------------- + ------------------------|
9 6 _________________ | 6 _________________|
/ 1205 ______ | / 1205 ______ |
27*3 / ---- + \/ 1057 | 27*3 / ---- + \/ 1057 |
\/ 27 \ \/ 27 /
$$x_{2} = - \frac{5}{9} + \frac{44}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} + \frac{\sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6} + \frac{44 \sqrt{3}}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}\right)$$
_________________
/ 1205 ______
3 / ---- + \/ 1057
5 88 \/ 27
x3 = - - - ------------------------ - ---------------------
9 _________________ 3
/ 1205 ______
27*3 / ---- + \/ 1057
\/ 27
$$x_{3} = - \frac{\sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{3} - \frac{88}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} - \frac{5}{9}$$
x3 = -(sqrt(1057) + 1205/27)^(1/3)/3 - 88/(27*(sqrt(1057) + 1205/27)^(1/3)) - 5/9
Suma y producto de raíces
[src]
suma
_________________ / _________________\ _________________ / _________________ \ _________________
/ 1205 ______ | ___ / 1205 ______ | / 1205 ______ | ___ / 1205 ______ | / 1205 ______
3 / ---- + \/ 1057 | ___ \/ 3 *3 / ---- + \/ 1057 | 3 / ---- + \/ 1057 | \/ 3 *3 / ---- + \/ 1057 ___ | 3 / ---- + \/ 1057
5 \/ 27 44 | 44*\/ 3 \/ 27 | 5 \/ 27 44 | \/ 27 44*\/ 3 | 5 88 \/ 27
- - + --------------------- + ------------------------ + I*|- ------------------------ + ---------------------------| + - - + --------------------- + ------------------------ + I*|- --------------------------- + ------------------------| + - - - ------------------------ - ---------------------
9 6 _________________ | _________________ 6 | 9 6 _________________ | 6 _________________| 9 _________________ 3
/ 1205 ______ | / 1205 ______ | / 1205 ______ | / 1205 ______ | / 1205 ______
27*3 / ---- + \/ 1057 | 27*3 / ---- + \/ 1057 | 27*3 / ---- + \/ 1057 | 27*3 / ---- + \/ 1057 | 27*3 / ---- + \/ 1057
\/ 27 \ \/ 27 / \/ 27 \ \/ 27 / \/ 27
$$\left(- \frac{\sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{3} - \frac{88}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} - \frac{5}{9}\right) + \left(\left(- \frac{5}{9} + \frac{44}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} + \frac{\sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6} + \frac{44 \sqrt{3}}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}\right)\right) + \left(- \frac{5}{9} + \frac{44}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} + \frac{\sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6} + i \left(- \frac{44 \sqrt{3}}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} + \frac{\sqrt{3} \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6}\right)\right)\right)$$
=
/ _________________\ / _________________ \
| ___ / 1205 ______ | | ___ / 1205 ______ |
| ___ \/ 3 *3 / ---- + \/ 1057 | | \/ 3 *3 / ---- + \/ 1057 ___ |
5 | 44*\/ 3 \/ 27 | | \/ 27 44*\/ 3 |
- - + I*|- ------------------------ + ---------------------------| + I*|- --------------------------- + ------------------------|
3 | _________________ 6 | | 6 _________________|
| / 1205 ______ | | / 1205 ______ |
| 27*3 / ---- + \/ 1057 | | 27*3 / ---- + \/ 1057 |
\ \/ 27 / \ \/ 27 /
$$- \frac{5}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6} + \frac{44 \sqrt{3}}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}\right) + i \left(- \frac{44 \sqrt{3}}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} + \frac{\sqrt{3} \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6}\right)$$
producto
/ _________________ / _________________\\ / _________________ / _________________ \\ / _________________\ | / 1205 ______ | ___ / 1205 ______ || | / 1205 ______ | ___ / 1205 ______ || | / 1205 ______ | | 3 / ---- + \/ 1057 | ___ \/ 3 *3 / ---- + \/ 1057 || | 3 / ---- + \/ 1057 | \/ 3 *3 / ---- + \/ 1057 ___ || | 3 / ---- + \/ 1057 | | 5 \/ 27 44 | 44*\/ 3 \/ 27 || | 5 \/ 27 44 | \/ 27 44*\/ 3 || | 5 88 \/ 27 | |- - + --------------------- + ------------------------ + I*|- ------------------------ + ---------------------------||*|- - + --------------------- + ------------------------ + I*|- --------------------------- + ------------------------||*|- - - ------------------------ - ---------------------| | 9 6 _________________ | _________________ 6 || | 9 6 _________________ | 6 _________________|| | 9 _________________ 3 | | / 1205 ______ | / 1205 ______ || | / 1205 ______ | / 1205 ______ || | / 1205 ______ | | 27*3 / ---- + \/ 1057 | 27*3 / ---- + \/ 1057 || | 27*3 / ---- + \/ 1057 | 27*3 / ---- + \/ 1057 || | 27*3 / ---- + \/ 1057 | \ \/ 27 \ \/ 27 // \ \/ 27 \ \/ 27 // \ \/ 27 /
$$\left(- \frac{5}{9} + \frac{44}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} + \frac{\sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6} + i \left(- \frac{44 \sqrt{3}}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} + \frac{\sqrt{3} \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6}\right)\right) \left(- \frac{5}{9} + \frac{44}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} + \frac{\sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{6} + \frac{44 \sqrt{3}}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}\right)\right) \left(- \frac{\sqrt[3]{\sqrt{1057} + \frac{1205}{27}}}{3} - \frac{88}{27 \sqrt[3]{\sqrt{1057} + \frac{1205}{27}}} - \frac{5}{9}\right)$$
=
-5/3
$$- \frac{5}{3}$$
-5/3
Respuesta numérica
[src]
x1 = 0.536749990764242 - 0.565804701556744*i
x2 = -2.74016664819515
x3 = 0.536749990764242 + 0.565804701556744*i
x3 = 0.536749990764242 + 0.565804701556744*i