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Ecuación 6*x^2+x-7=0
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Ecuación (6*x+8)/2+5=5*x/3
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Ecuación 2+3x=−2x−13
- Expresar {x} en función de y en la ecuación:
- 6*x+4*y=15
- -4*x+4*y=-9
- 3*x-12*y=-14
- 1*x+4*y=-16
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Expresiones idénticas
- x^ tres - nueve *x^ dos + seis *x- quince = cero
- x al cubo menos 9 multiplicar por x al cuadrado más 6 multiplicar por x menos 15 es igual a 0
- x en el grado tres menos nueve multiplicar por x en el grado dos más seis multiplicar por x menos quince es igual a cero
- x3-9*x2+6*x-15=0
- x³-9*x²+6*x-15=0
- x en el grado 3-9*x en el grado 2+6*x-15=0
- x^3-9x^2+6x-15=0
- x3-9x2+6x-15=0
- x^3-9*x^2+6*x-15=O
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Expresiones semejantes
- x^3-9*x^2+6*x+15=0
- x^3-9*x^2-6*x-15=0
- x^3+9*x^2+6*x-15=0
x^3-9*x^2+6*x-15=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 x - 9*x + 6*x - 15 = 0
$$\left(6 x + \left(x^{3} - 9 x^{2}\right)\right) - 15 = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -9$$
$$q = \frac{c}{a}$$
$$q = 6$$
$$v = \frac{d}{a}$$
$$v = -15$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 9$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 6$$
$$x_{1} x_{2} x_{3} = -15$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -9$$
$$q = \frac{c}{a}$$
$$q = 6$$
$$v = \frac{d}{a}$$
$$v = -15$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 9$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 6$$
$$x_{1} x_{2} x_{3} = -15$$
Respuesta rápida
[src]
_______________ / _______________ \
/ ______ | / ______ |
/ 51 \/ 1229 | ___ / 51 \/ 1229 |
3 / -- + -------- | \/ 3 *3 / -- + -------- ___ |
7 \/ 2 2 | \/ 2 2 7*\/ 3 |
x1 = 3 - ---------------------- - -------------------- + I*|- -------------------------- + ----------------------|
_______________ 2 | 2 _______________|
/ ______ | / ______ |
/ 51 \/ 1229 | / 51 \/ 1229 |
2*3 / -- + -------- | 2*3 / -- + -------- |
\/ 2 2 \ \/ 2 2 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2} - \frac{7}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + 3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2} + \frac{7 \sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}\right)$$
_______________ / _______________ \
/ ______ | / ______ |
/ 51 \/ 1229 | ___ / 51 \/ 1229 |
3 / -- + -------- |\/ 3 *3 / -- + -------- ___ |
7 \/ 2 2 | \/ 2 2 7*\/ 3 |
x2 = 3 - ---------------------- - -------------------- + I*|-------------------------- - ----------------------|
_______________ 2 | 2 _______________|
/ ______ | / ______ |
/ 51 \/ 1229 | / 51 \/ 1229 |
2*3 / -- + -------- | 2*3 / -- + -------- |
\/ 2 2 \ \/ 2 2 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2} - \frac{7}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + 3 + i \left(- \frac{7 \sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2}\right)$$
_______________
/ ______
/ 51 \/ 1229 7
x3 = 3 + 3 / -- + -------- + --------------------
\/ 2 2 _______________
/ ______
/ 51 \/ 1229
3 / -- + --------
\/ 2 2
$$x_{3} = \frac{7}{\sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + 3 + \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}$$
x3 = 7/(sqrt(1229)/2 + 51/2)^(1/3) + 3 + (sqrt(1229)/2 + 51/2)^(1/3)
Suma y producto de raíces
[src]
suma
_______________ / _______________ \ _______________ / _______________ \
/ ______ | / ______ | / ______ | / ______ |
/ 51 \/ 1229 | ___ / 51 \/ 1229 | / 51 \/ 1229 | ___ / 51 \/ 1229 | _______________
3 / -- + -------- | \/ 3 *3 / -- + -------- ___ | 3 / -- + -------- |\/ 3 *3 / -- + -------- ___ | / ______
7 \/ 2 2 | \/ 2 2 7*\/ 3 | 7 \/ 2 2 | \/ 2 2 7*\/ 3 | / 51 \/ 1229 7
3 - ---------------------- - -------------------- + I*|- -------------------------- + ----------------------| + 3 - ---------------------- - -------------------- + I*|-------------------------- - ----------------------| + 3 + 3 / -- + -------- + --------------------
_______________ 2 | 2 _______________| _______________ 2 | 2 _______________| \/ 2 2 _______________
/ ______ | / ______ | / ______ | / ______ | / ______
/ 51 \/ 1229 | / 51 \/ 1229 | / 51 \/ 1229 | / 51 \/ 1229 | / 51 \/ 1229
2*3 / -- + -------- | 2*3 / -- + -------- | 2*3 / -- + -------- | 2*3 / -- + -------- | 3 / -- + --------
\/ 2 2 \ \/ 2 2 / \/ 2 2 \ \/ 2 2 / \/ 2 2
$$\left(\frac{7}{\sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + 3 + \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2} - \frac{7}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + 3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2} + \frac{7 \sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2} - \frac{7}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + 3 + i \left(- \frac{7 \sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2}\right)\right)\right)$$
=
/ _______________ \ / _______________ \
| / ______ | | / ______ |
| ___ / 51 \/ 1229 | | ___ / 51 \/ 1229 |
|\/ 3 *3 / -- + -------- ___ | | \/ 3 *3 / -- + -------- ___ |
| \/ 2 2 7*\/ 3 | | \/ 2 2 7*\/ 3 |
9 + I*|-------------------------- - ----------------------| + I*|- -------------------------- + ----------------------|
| 2 _______________| | 2 _______________|
| / ______ | | / ______ |
| / 51 \/ 1229 | | / 51 \/ 1229 |
| 2*3 / -- + -------- | | 2*3 / -- + -------- |
\ \/ 2 2 / \ \/ 2 2 /
$$9 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2} + \frac{7 \sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}\right) + i \left(- \frac{7 \sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2}\right)$$
producto
/ _______________ / _______________ \\ / _______________ / _______________ \\ | / ______ | / ______ || | / ______ | / ______ || | / 51 \/ 1229 | ___ / 51 \/ 1229 || | / 51 \/ 1229 | ___ / 51 \/ 1229 || / _______________ \ | 3 / -- + -------- | \/ 3 *3 / -- + -------- ___ || | 3 / -- + -------- |\/ 3 *3 / -- + -------- ___ || | / ______ | | 7 \/ 2 2 | \/ 2 2 7*\/ 3 || | 7 \/ 2 2 | \/ 2 2 7*\/ 3 || | / 51 \/ 1229 7 | |3 - ---------------------- - -------------------- + I*|- -------------------------- + ----------------------||*|3 - ---------------------- - -------------------- + I*|-------------------------- - ----------------------||*|3 + 3 / -- + -------- + --------------------| | _______________ 2 | 2 _______________|| | _______________ 2 | 2 _______________|| | \/ 2 2 _______________| | / ______ | / ______ || | / ______ | / ______ || | / ______ | | / 51 \/ 1229 | / 51 \/ 1229 || | / 51 \/ 1229 | / 51 \/ 1229 || | / 51 \/ 1229 | | 2*3 / -- + -------- | 2*3 / -- + -------- || | 2*3 / -- + -------- | 2*3 / -- + -------- || | 3 / -- + -------- | \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2} - \frac{7}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + 3 + i \left(- \frac{7 \sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2} - \frac{7}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + 3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}{2} + \frac{7 \sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}}\right)\right) \left(\frac{7}{\sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}} + 3 + \sqrt[3]{\frac{\sqrt{1229}}{2} + \frac{51}{2}}\right)$$
=
15
$$15$$
15
Respuesta numérica
[src]
x1 = 8.5017913555054
x2 = 0.2491043222473 + 1.30471494573928*i
x3 = 0.2491043222473 - 1.30471494573928*i
x3 = 0.2491043222473 - 1.30471494573928*i