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- La ecuación:
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Ecuación x^3-x^2-x-1=0
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Ecuación 3x-2(3x+4)=10
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Ecuación 12-4(x-3)=39-9x
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Ecuación 0,2x+2,7=1,4-1,1x
- Expresar {x} en función de y en la ecuación:
- -11*x-3*y=14
- 2*x-15*y=-1
- -18*x-6*y=-1
- 6*x+9*y=-9
- Gráfico de la función y =:
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x^3-6x^2+9x-5
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Expresiones idénticas
- x^ tres -6x^ dos +9x- cinco = cero
- x al cubo menos 6x al cuadrado más 9x menos 5 es igual a 0
- x en el grado tres menos 6x en el grado dos más 9x menos cinco es igual a cero
- x3-6x2+9x-5=0
- x³-6x²+9x-5=0
- x en el grado 3-6x en el grado 2+9x-5=0
- x^3-6x^2+9x-5=O
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Expresiones semejantes
- x^3-6x^2+9x+5=0
- x^3+6x^2+9x-5=0
- x^3-6x^2-9x-5=0
x^3-6x^2+9x-5=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 x - 6*x + 9*x - 5 = 0
$$\left(9 x + \left(x^{3} - 6 x^{2}\right)\right) - 5 = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 9$$
$$v = \frac{d}{a}$$
$$v = -5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 6$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 9$$
$$x_{1} x_{2} x_{3} = -5$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 9$$
$$v = \frac{d}{a}$$
$$v = -5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 6$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 9$$
$$x_{1} x_{2} x_{3} = -5$$
Respuesta rápida
[src]
___________ / ___________\
/ ___ | / ___ |
/ 3 \/ 5 | ___ / 3 \/ 5 |
3 / - + ----- | ___ \/ 3 *3 / - + ----- |
1 \/ 2 2 | \/ 3 \/ 2 2 |
x1 = 2 - ------------------ - ---------------- + I*|------------------ - ----------------------|
___________ 2 | ___________ 2 |
/ ___ | / ___ |
/ 3 \/ 5 | / 3 \/ 5 |
2*3 / - + ----- |2*3 / - + ----- |
\/ 2 2 \ \/ 2 2 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + 2 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2} + \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}\right)$$
___________ / ___________ \
/ ___ | / ___ |
/ 3 \/ 5 | ___ / 3 \/ 5 |
3 / - + ----- |\/ 3 *3 / - + ----- ___ |
1 \/ 2 2 | \/ 2 2 \/ 3 |
x2 = 2 - ------------------ - ---------------- + I*|---------------------- - ------------------|
___________ 2 | 2 ___________|
/ ___ | / ___ |
/ 3 \/ 5 | / 3 \/ 5 |
2*3 / - + ----- | 2*3 / - + ----- |
\/ 2 2 \ \/ 2 2 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + 2 + i \left(- \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2}\right)$$
___________
/ ___
1 / 3 \/ 5
x3 = 2 + ---------------- + 3 / - + -----
___________ \/ 2 2
/ ___
/ 3 \/ 5
3 / - + -----
\/ 2 2
$$x_{3} = \frac{1}{\sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}} + 2$$
x3 = (sqrt(5)/2 + 3/2)^(-1/3) + (sqrt(5)/2 + 3/2)^(1/3) + 2
Suma y producto de raíces
[src]
suma
___________ / ___________\ ___________ / ___________ \
/ ___ | / ___ | / ___ | / ___ |
/ 3 \/ 5 | ___ / 3 \/ 5 | / 3 \/ 5 | ___ / 3 \/ 5 | ___________
3 / - + ----- | ___ \/ 3 *3 / - + ----- | 3 / - + ----- |\/ 3 *3 / - + ----- ___ | / ___
1 \/ 2 2 | \/ 3 \/ 2 2 | 1 \/ 2 2 | \/ 2 2 \/ 3 | 1 / 3 \/ 5
2 - ------------------ - ---------------- + I*|------------------ - ----------------------| + 2 - ------------------ - ---------------- + I*|---------------------- - ------------------| + 2 + ---------------- + 3 / - + -----
___________ 2 | ___________ 2 | ___________ 2 | 2 ___________| ___________ \/ 2 2
/ ___ | / ___ | / ___ | / ___ | / ___
/ 3 \/ 5 | / 3 \/ 5 | / 3 \/ 5 | / 3 \/ 5 | / 3 \/ 5
2*3 / - + ----- |2*3 / - + ----- | 2*3 / - + ----- | 2*3 / - + ----- | 3 / - + -----
\/ 2 2 \ \/ 2 2 / \/ 2 2 \ \/ 2 2 / \/ 2 2
$$\left(\frac{1}{\sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}} + 2\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + 2 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2} + \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + 2 + i \left(- \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2}\right)\right)\right)$$
=
/ ___________\ / ___________ \
| / ___ | | / ___ |
| ___ / 3 \/ 5 | | ___ / 3 \/ 5 |
| ___ \/ 3 *3 / - + ----- | |\/ 3 *3 / - + ----- ___ |
| \/ 3 \/ 2 2 | | \/ 2 2 \/ 3 |
6 + I*|------------------ - ----------------------| + I*|---------------------- - ------------------|
| ___________ 2 | | 2 ___________|
| / ___ | | / ___ |
| / 3 \/ 5 | | / 3 \/ 5 |
|2*3 / - + ----- | | 2*3 / - + ----- |
\ \/ 2 2 / \ \/ 2 2 /
$$6 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2} + \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}\right) + i \left(- \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2}\right)$$
producto
/ ___________ / ___________\\ / ___________ / ___________ \\ | / ___ | / ___ || | / ___ | / ___ || | / 3 \/ 5 | ___ / 3 \/ 5 || | / 3 \/ 5 | ___ / 3 \/ 5 || / ___________\ | 3 / - + ----- | ___ \/ 3 *3 / - + ----- || | 3 / - + ----- |\/ 3 *3 / - + ----- ___ || | / ___ | | 1 \/ 2 2 | \/ 3 \/ 2 2 || | 1 \/ 2 2 | \/ 2 2 \/ 3 || | 1 / 3 \/ 5 | |2 - ------------------ - ---------------- + I*|------------------ - ----------------------||*|2 - ------------------ - ---------------- + I*|---------------------- - ------------------||*|2 + ---------------- + 3 / - + ----- | | ___________ 2 | ___________ 2 || | ___________ 2 | 2 ___________|| | ___________ \/ 2 2 | | / ___ | / ___ || | / ___ | / ___ || | / ___ | | / 3 \/ 5 | / 3 \/ 5 || | / 3 \/ 5 | / 3 \/ 5 || | / 3 \/ 5 | | 2*3 / - + ----- |2*3 / - + ----- || | 2*3 / - + ----- | 2*3 / - + ----- || | 3 / - + ----- | \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + 2 + i \left(- \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + 2 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}{2} + \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}}\right)\right) \left(\frac{1}{\sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}}} + \sqrt[3]{\frac{\sqrt{5}}{2} + \frac{3}{2}} + 2\right)$$
=
5
$$5$$
5
Respuesta numérica
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x1 = 4.10380340273554
x2 = 0.948098298632232 - 0.565235851677171*i
x3 = 0.948098298632232 + 0.565235851677171*i
x3 = 0.948098298632232 + 0.565235851677171*i