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Ecuación (x+9)^2=36*x
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Ecuación a+120=2000/5
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Ecuación -x/11+x=50/11
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Ecuación x^2+7x+6=0
- Expresar {x} en función de y en la ecuación:
- 12*x+8*y=18
- 8*x+6*y=20
- -2*x+18*y=13
- -11*x-1*y=15
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Expresiones idénticas
- x^ tres - tres *x^ dos -x- tres = cero
- x al cubo menos 3 multiplicar por x al cuadrado menos x menos 3 es igual a 0
- x en el grado tres menos tres multiplicar por x en el grado dos menos x menos tres es igual a cero
- x3-3*x2-x-3=0
- x³-3*x²-x-3=0
- x en el grado 3-3*x en el grado 2-x-3=0
- x^3-3x^2-x-3=0
- x3-3x2-x-3=0
- x^3-3*x^2-x-3=O
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Expresiones semejantes
- x^3-3*x^2-x+3=0
- x^3+3*x^2-x-3=0
- x^3-3*x^2+x-3=0
x^3-3*x^2-x-3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 x - 3*x - x - 3 = 0
$$\left(- x + \left(x^{3} - 3 x^{2}\right)\right) - 3 = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = -1$$
$$v = \frac{d}{a}$$
$$v = -3$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 3$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -1$$
$$x_{1} x_{2} x_{3} = -3$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = -1$$
$$v = \frac{d}{a}$$
$$v = -3$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 3$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -1$$
$$x_{1} x_{2} x_{3} = -3$$
Respuesta rápida
[src]
_____________ / _____________ \
/ _____ | / _____ |
/ \/ 537 | ___ / \/ 537 |
3 / 3 + ------- | \/ 3 *3 / 3 + ------- ___ |
2 \/ 9 | \/ 9 2*\/ 3 |
x1 = 1 - -------------------- - ------------------ + I*|- ------------------------ + --------------------|
_____________ 2 | 2 _____________|
/ _____ | / _____ |
/ \/ 537 | / \/ 537 |
3*3 / 3 + ------- | 3*3 / 3 + ------- |
\/ 9 \ \/ 9 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2} + \frac{2 \sqrt{3}}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}\right)$$
_____________ / _____________ \
/ _____ | / _____ |
/ \/ 537 | ___ / \/ 537 |
3 / 3 + ------- |\/ 3 *3 / 3 + ------- ___ |
2 \/ 9 | \/ 9 2*\/ 3 |
x2 = 1 - -------------------- - ------------------ + I*|------------------------ - --------------------|
_____________ 2 | 2 _____________|
/ _____ | / _____ |
/ \/ 537 | / \/ 537 |
3*3 / 3 + ------- | 3*3 / 3 + ------- |
\/ 9 \ \/ 9 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + 1 + i \left(- \frac{2 \sqrt{3}}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2}\right)$$
_____________
/ _____
/ \/ 537 4
x3 = 1 + 3 / 3 + ------- + --------------------
\/ 9 _____________
/ _____
/ \/ 537
3*3 / 3 + -------
\/ 9
$$x_{3} = \frac{4}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + 1 + \sqrt[3]{\frac{\sqrt{537}}{9} + 3}$$
x3 = 4/(3*(sqrt(537)/9 + 3)^(1/3)) + 1 + (sqrt(537)/9 + 3)^(1/3)
Suma y producto de raíces
[src]
suma
_____________ / _____________ \ _____________ / _____________ \
/ _____ | / _____ | / _____ | / _____ |
/ \/ 537 | ___ / \/ 537 | / \/ 537 | ___ / \/ 537 | _____________
3 / 3 + ------- | \/ 3 *3 / 3 + ------- ___ | 3 / 3 + ------- |\/ 3 *3 / 3 + ------- ___ | / _____
2 \/ 9 | \/ 9 2*\/ 3 | 2 \/ 9 | \/ 9 2*\/ 3 | / \/ 537 4
1 - -------------------- - ------------------ + I*|- ------------------------ + --------------------| + 1 - -------------------- - ------------------ + I*|------------------------ - --------------------| + 1 + 3 / 3 + ------- + --------------------
_____________ 2 | 2 _____________| _____________ 2 | 2 _____________| \/ 9 _____________
/ _____ | / _____ | / _____ | / _____ | / _____
/ \/ 537 | / \/ 537 | / \/ 537 | / \/ 537 | / \/ 537
3*3 / 3 + ------- | 3*3 / 3 + ------- | 3*3 / 3 + ------- | 3*3 / 3 + ------- | 3*3 / 3 + -------
\/ 9 \ \/ 9 / \/ 9 \ \/ 9 / \/ 9
$$\left(\frac{4}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + 1 + \sqrt[3]{\frac{\sqrt{537}}{9} + 3}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2} + \frac{2 \sqrt{3}}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + 1 + i \left(- \frac{2 \sqrt{3}}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2}\right)\right)\right)$$
=
/ _____________ \ / _____________ \
| / _____ | | / _____ |
| ___ / \/ 537 | | ___ / \/ 537 |
|\/ 3 *3 / 3 + ------- ___ | | \/ 3 *3 / 3 + ------- ___ |
| \/ 9 2*\/ 3 | | \/ 9 2*\/ 3 |
3 + I*|------------------------ - --------------------| + I*|- ------------------------ + --------------------|
| 2 _____________| | 2 _____________|
| / _____ | | / _____ |
| / \/ 537 | | / \/ 537 |
| 3*3 / 3 + ------- | | 3*3 / 3 + ------- |
\ \/ 9 / \ \/ 9 /
$$3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2} + \frac{2 \sqrt{3}}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}\right) + i \left(- \frac{2 \sqrt{3}}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2}\right)$$
producto
/ _____________ / _____________ \\ / _____________ / _____________ \\ | / _____ | / _____ || | / _____ | / _____ || | / \/ 537 | ___ / \/ 537 || | / \/ 537 | ___ / \/ 537 || / _____________ \ | 3 / 3 + ------- | \/ 3 *3 / 3 + ------- ___ || | 3 / 3 + ------- |\/ 3 *3 / 3 + ------- ___ || | / _____ | | 2 \/ 9 | \/ 9 2*\/ 3 || | 2 \/ 9 | \/ 9 2*\/ 3 || | / \/ 537 4 | |1 - -------------------- - ------------------ + I*|- ------------------------ + --------------------||*|1 - -------------------- - ------------------ + I*|------------------------ - --------------------||*|1 + 3 / 3 + ------- + --------------------| | _____________ 2 | 2 _____________|| | _____________ 2 | 2 _____________|| | \/ 9 _____________| | / _____ | / _____ || | / _____ | / _____ || | / _____ | | / \/ 537 | / \/ 537 || | / \/ 537 | / \/ 537 || | / \/ 537 | | 3*3 / 3 + ------- | 3*3 / 3 + ------- || | 3*3 / 3 + ------- | 3*3 / 3 + ------- || | 3*3 / 3 + ------- | \ \/ 9 \ \/ 9 // \ \/ 9 \ \/ 9 // \ \/ 9 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + 1 + i \left(- \frac{2 \sqrt{3}}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}{2} + \frac{2 \sqrt{3}}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}}\right)\right) \left(\frac{4}{3 \sqrt[3]{\frac{\sqrt{537}}{9} + 3}} + 1 + \sqrt[3]{\frac{\sqrt{537}}{9} + 3}\right)$$
=
3
$$3$$
3
Respuesta numérica
[src]
x1 = -0.26255112740716 - 0.884367597750661*i
x2 = -0.26255112740716 + 0.884367597750661*i
x3 = 3.52510225481432
x3 = 3.52510225481432
Gráfico