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Expresiones idénticas
- x^ tres + dos *x- ciento veintiséis = cero
- x al cubo más 2 multiplicar por x menos 126 es igual a 0
- x en el grado tres más dos multiplicar por x menos ciento veintiséis es igual a cero
- x3+2*x-126=0
- x³+2*x-126=0
- x en el grado 3+2*x-126=0
- x^3+2x-126=0
- x3+2x-126=0
- x^3+2*x-126=O
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Expresiones semejantes
- x^3-2*x-126=0
- x^3+2*x+126=0
x^3+2*x-126=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
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2$$
$$v = \frac{d}{a}$$
$$v = -126$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 2$$
$$x_{1} x_{2} x_{3} = -126$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2$$
$$v = \frac{d}{a}$$
$$v = -126$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 2$$
$$x_{1} x_{2} x_{3} = -126$$
Suma y producto de raíces
[src]
suma
_________________ / _________________ \ _________________ / _________________ \
/ ________ | / ________ | / ________ | / ________ |
/ \/ 321513 | ___ / \/ 321513 | / \/ 321513 | ___ / \/ 321513 | _________________
3 / 63 + ---------- | \/ 3 *3 / 63 + ---------- ___ | 3 / 63 + ---------- |\/ 3 *3 / 63 + ---------- ___ | / ________
\/ 9 1 | \/ 9 \/ 3 | \/ 9 1 | \/ 9 \/ 3 | / \/ 321513 2
- ---------------------- + ------------------------ + I*|- ---------------------------- - ------------------------| + - ---------------------- + ------------------------ + I*|---------------------------- + ------------------------| + 3 / 63 + ---------- - ------------------------
2 _________________ | 2 _________________| 2 _________________ | 2 _________________| \/ 9 _________________
/ ________ | / ________ | / ________ | / ________ | / ________
/ \/ 321513 | / \/ 321513 | / \/ 321513 | / \/ 321513 | / \/ 321513
3*3 / 63 + ---------- | 3*3 / 63 + ---------- | 3*3 / 63 + ---------- | 3*3 / 63 + ---------- | 3*3 / 63 + ----------
\/ 9 \ \/ 9 / \/ 9 \ \/ 9 / \/ 9
$$\left(- \frac{2}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}\right) + \left(\left(- \frac{\sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2} + \frac{1}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}\right)\right) + \left(- \frac{\sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2} + \frac{1}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + \frac{\sqrt{3} \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2}\right)\right)\right)$$
=
/ _________________ \ / _________________ \ | / ________ | | / ________ | | ___ / \/ 321513 | | ___ / \/ 321513 | |\/ 3 *3 / 63 + ---------- ___ | | \/ 3 *3 / 63 + ---------- ___ | | \/ 9 \/ 3 | | \/ 9 \/ 3 | I*|---------------------------- + ------------------------| + I*|- ---------------------------- - ------------------------| | 2 _________________| | 2 _________________| | / ________ | | / ________ | | / \/ 321513 | | / \/ 321513 | | 3*3 / 63 + ---------- | | 3*3 / 63 + ---------- | \ \/ 9 / \ \/ 9 /
$$i \left(- \frac{\sqrt{3} \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}\right) + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + \frac{\sqrt{3} \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2}\right)$$
producto
/ _________________ / _________________ \\ / _________________ / _________________ \\ | / ________ | / ________ || | / ________ | / ________ || | / \/ 321513 | ___ / \/ 321513 || | / \/ 321513 | ___ / \/ 321513 || / _________________ \ | 3 / 63 + ---------- | \/ 3 *3 / 63 + ---------- ___ || | 3 / 63 + ---------- |\/ 3 *3 / 63 + ---------- ___ || | / ________ | | \/ 9 1 | \/ 9 \/ 3 || | \/ 9 1 | \/ 9 \/ 3 || | / \/ 321513 2 | |- ---------------------- + ------------------------ + I*|- ---------------------------- - ------------------------||*|- ---------------------- + ------------------------ + I*|---------------------------- + ------------------------||*|3 / 63 + ---------- - ------------------------| | 2 _________________ | 2 _________________|| | 2 _________________ | 2 _________________|| |\/ 9 _________________| | / ________ | / ________ || | / ________ | / ________ || | / ________ | | / \/ 321513 | / \/ 321513 || | / \/ 321513 | / \/ 321513 || | / \/ 321513 | | 3*3 / 63 + ---------- | 3*3 / 63 + ---------- || | 3*3 / 63 + ---------- | 3*3 / 63 + ---------- || | 3*3 / 63 + ---------- | \ \/ 9 \ \/ 9 // \ \/ 9 \ \/ 9 // \ \/ 9 /
$$\left(- \frac{\sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2} + \frac{1}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + \frac{\sqrt{3} \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2}\right)\right) \left(- \frac{\sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2} + \frac{1}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}\right)\right) \left(- \frac{2}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}\right)$$
=
126
$$126$$
126
Respuesta rápida
[src]
_________________ / _________________ \
/ ________ | / ________ |
/ \/ 321513 | ___ / \/ 321513 |
3 / 63 + ---------- | \/ 3 *3 / 63 + ---------- ___ |
\/ 9 1 | \/ 9 \/ 3 |
x1 = - ---------------------- + ------------------------ + I*|- ---------------------------- - ------------------------|
2 _________________ | 2 _________________|
/ ________ | / ________ |
/ \/ 321513 | / \/ 321513 |
3*3 / 63 + ---------- | 3*3 / 63 + ---------- |
\/ 9 \ \/ 9 /
$$x_{1} = - \frac{\sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2} + \frac{1}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}\right)$$
_________________ / _________________ \
/ ________ | / ________ |
/ \/ 321513 | ___ / \/ 321513 |
3 / 63 + ---------- |\/ 3 *3 / 63 + ---------- ___ |
\/ 9 1 | \/ 9 \/ 3 |
x2 = - ---------------------- + ------------------------ + I*|---------------------------- + ------------------------|
2 _________________ | 2 _________________|
/ ________ | / ________ |
/ \/ 321513 | / \/ 321513 |
3*3 / 63 + ---------- | 3*3 / 63 + ---------- |
\/ 9 \ \/ 9 /
$$x_{2} = - \frac{\sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2} + \frac{1}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + \frac{\sqrt{3} \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}}{2}\right)$$
_________________
/ ________
/ \/ 321513 2
x3 = 3 / 63 + ---------- - ------------------------
\/ 9 _________________
/ ________
/ \/ 321513
3*3 / 63 + ----------
\/ 9
$$x_{3} = - \frac{2}{3 \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}} + \sqrt[3]{63 + \frac{\sqrt{321513}}{9}}$$
x3 = -2/(3*(63 + sqrt(321513)/9)^(1/3)) + (63 + sqrt(321513)/9)^(1/3)
Respuesta numérica
[src]
x1 = -2.44017514353687 + 4.45683342670618*i
x2 = 4.88035028707374
x3 = -2.44017514353687 - 4.45683342670618*i
x3 = -2.44017514353687 - 4.45683342670618*i