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Ecuación x^(5/3)=32
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Ecuación 2+x=6
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Expresiones idénticas
- x^ tres -x^ dos - mil doscientos sesenta = cero
- x al cubo menos x al cuadrado menos 1260 es igual a 0
- x en el grado tres menos x en el grado dos menos mil doscientos sesenta es igual a cero
- x3-x2-1260=0
- x³-x²-1260=0
- x en el grado 3-x en el grado 2-1260=0
- x^3-x^2-1260=O
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Expresiones semejantes
- x^3+x^2-1260=0
- x^3-x^2+1260=0
x^3-x^2-1260=0 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
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = -1260$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 1$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = -1260$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = -1260$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 1$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = -1260$$
Respuesta rápida
[src]
______________________ / ______________________ \
/ ________ | / ________ |
/ 17011 2*\/ 893130 | ___ / 17011 2*\/ 893130 |
3 / ----- + ------------ | \/ 3 *3 / ----- + ------------ ___ |
1 \/ 27 3 1 | \/ 27 3 \/ 3 |
x1 = - - --------------------------- - ------------------------------ + I*|- --------------------------------- + ------------------------------|
3 2 ______________________ | 2 ______________________|
/ ________ | / ________ |
/ 17011 2*\/ 893130 | / 17011 2*\/ 893130 |
18*3 / ----- + ------------ | 18*3 / ----- + ------------ |
\/ 27 3 \ \/ 27 3 /
$$x_{1} = - \frac{\sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2} - \frac{1}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2} + \frac{\sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}\right)$$
______________________ / ______________________ \
/ ________ | / ________ |
/ 17011 2*\/ 893130 | ___ / 17011 2*\/ 893130 |
3 / ----- + ------------ |\/ 3 *3 / ----- + ------------ ___ |
1 \/ 27 3 1 | \/ 27 3 \/ 3 |
x2 = - - --------------------------- - ------------------------------ + I*|--------------------------------- - ------------------------------|
3 2 ______________________ | 2 ______________________|
/ ________ | / ________ |
/ 17011 2*\/ 893130 | / 17011 2*\/ 893130 |
18*3 / ----- + ------------ | 18*3 / ----- + ------------ |
\/ 27 3 \ \/ 27 3 /
$$x_{2} = - \frac{\sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2} - \frac{1}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2}\right)$$
______________________
/ ________
1 / 17011 2*\/ 893130 1
x3 = - + 3 / ----- + ------------ + -----------------------------
3 \/ 27 3 ______________________
/ ________
/ 17011 2*\/ 893130
9*3 / ----- + ------------
\/ 27 3
$$x_{3} = \frac{1}{9 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{1}{3} + \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}$$
x3 = 1/(9*(2*sqrt(893130)/3 + 17011/27)^(1/3)) + 1/3 + (2*sqrt(893130)/3 + 17011/27)^(1/3)
Suma y producto de raíces
[src]
suma
______________________ / ______________________ \ ______________________ / ______________________ \
/ ________ | / ________ | / ________ | / ________ |
/ 17011 2*\/ 893130 | ___ / 17011 2*\/ 893130 | / 17011 2*\/ 893130 | ___ / 17011 2*\/ 893130 | ______________________
3 / ----- + ------------ | \/ 3 *3 / ----- + ------------ ___ | 3 / ----- + ------------ |\/ 3 *3 / ----- + ------------ ___ | / ________
1 \/ 27 3 1 | \/ 27 3 \/ 3 | 1 \/ 27 3 1 | \/ 27 3 \/ 3 | 1 / 17011 2*\/ 893130 1
- - --------------------------- - ------------------------------ + I*|- --------------------------------- + ------------------------------| + - - --------------------------- - ------------------------------ + I*|--------------------------------- - ------------------------------| + - + 3 / ----- + ------------ + -----------------------------
3 2 ______________________ | 2 ______________________| 3 2 ______________________ | 2 ______________________| 3 \/ 27 3 ______________________
/ ________ | / ________ | / ________ | / ________ | / ________
/ 17011 2*\/ 893130 | / 17011 2*\/ 893130 | / 17011 2*\/ 893130 | / 17011 2*\/ 893130 | / 17011 2*\/ 893130
18*3 / ----- + ------------ | 18*3 / ----- + ------------ | 18*3 / ----- + ------------ | 18*3 / ----- + ------------ | 9*3 / ----- + ------------
\/ 27 3 \ \/ 27 3 / \/ 27 3 \ \/ 27 3 / \/ 27 3
$$\left(\frac{1}{9 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{1}{3} + \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2} - \frac{1}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2} + \frac{\sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2} - \frac{1}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2}\right)\right)\right)$$
=
/ ______________________ \ / ______________________ \
| / ________ | | / ________ |
| ___ / 17011 2*\/ 893130 | | ___ / 17011 2*\/ 893130 |
|\/ 3 *3 / ----- + ------------ ___ | | \/ 3 *3 / ----- + ------------ ___ |
| \/ 27 3 \/ 3 | | \/ 27 3 \/ 3 |
1 + I*|--------------------------------- - ------------------------------| + I*|- --------------------------------- + ------------------------------|
| 2 ______________________| | 2 ______________________|
| / ________ | | / ________ |
| / 17011 2*\/ 893130 | | / 17011 2*\/ 893130 |
| 18*3 / ----- + ------------ | | 18*3 / ----- + ------------ |
\ \/ 27 3 / \ \/ 27 3 /
$$1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2} + \frac{\sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}\right) + i \left(- \frac{\sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2}\right)$$
producto
/ ______________________ / ______________________ \\ / ______________________ / ______________________ \\ | / ________ | / ________ || | / ________ | / ________ || | / 17011 2*\/ 893130 | ___ / 17011 2*\/ 893130 || | / 17011 2*\/ 893130 | ___ / 17011 2*\/ 893130 || / ______________________ \ | 3 / ----- + ------------ | \/ 3 *3 / ----- + ------------ ___ || | 3 / ----- + ------------ |\/ 3 *3 / ----- + ------------ ___ || | / ________ | |1 \/ 27 3 1 | \/ 27 3 \/ 3 || |1 \/ 27 3 1 | \/ 27 3 \/ 3 || |1 / 17011 2*\/ 893130 1 | |- - --------------------------- - ------------------------------ + I*|- --------------------------------- + ------------------------------||*|- - --------------------------- - ------------------------------ + I*|--------------------------------- - ------------------------------||*|- + 3 / ----- + ------------ + -----------------------------| |3 2 ______________________ | 2 ______________________|| |3 2 ______________________ | 2 ______________________|| |3 \/ 27 3 ______________________| | / ________ | / ________ || | / ________ | / ________ || | / ________ | | / 17011 2*\/ 893130 | / 17011 2*\/ 893130 || | / 17011 2*\/ 893130 | / 17011 2*\/ 893130 || | / 17011 2*\/ 893130 | | 18*3 / ----- + ------------ | 18*3 / ----- + ------------ || | 18*3 / ----- + ------------ | 18*3 / ----- + ------------ || | 9*3 / ----- + ------------ | \ \/ 27 3 \ \/ 27 3 // \ \/ 27 3 \ \/ 27 3 // \ \/ 27 3 /
$$\left(- \frac{\sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2} - \frac{1}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2} - \frac{1}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}{2} + \frac{\sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}}\right)\right) \left(\frac{1}{9 \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}} + \frac{1}{3} + \sqrt[3]{\frac{2 \sqrt{893130}}{3} + \frac{17011}{27}}\right)$$
=
1260
$$1260$$
1260
Respuesta numérica
[src]
x1 = -5.0723275226583 - 9.34506150523725*i
x2 = 11.1446550453166
x3 = -5.0723275226583 + 9.34506150523725*i
x3 = -5.0723275226583 + 9.34506150523725*i