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Expresiones idénticas
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- x3-x2-x+5=0
- x³-x²-x+5=0
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- x^3-x^2-x+5=O
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Expresiones semejantes
- x^3-x^2-x-5=0
- x^3+x^2-x+5=0
- x^3-x^2+x+5=0
x^3-x^2-x+5=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 x - x - x + 5 = 0
$$\left(- x + \left(x^{3} - x^{2}\right)\right) + 5 = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -1$$
$$v = \frac{d}{a}$$
$$v = 5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 1$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -1$$
$$x_{1} x_{2} x_{3} = 5$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -1$$
$$v = \frac{d}{a}$$
$$v = 5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 1$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -1$$
$$x_{1} x_{2} x_{3} = 5$$
Suma y producto de raíces
[src]
suma
________________ / ________________\ ________________ / ________________ \ ________________
3 / _____ | ___ ___ 3 / _____ | 3 / _____ | ___ 3 / _____ ___ | 3 / _____
1 \/ 62 + 6*\/ 105 2 | 2*\/ 3 \/ 3 *\/ 62 + 6*\/ 105 | 1 \/ 62 + 6*\/ 105 2 | \/ 3 *\/ 62 + 6*\/ 105 2*\/ 3 | 1 4 \/ 62 + 6*\/ 105
- + ------------------- + --------------------- + I*|- --------------------- + -------------------------| + - + ------------------- + --------------------- + I*|- ------------------------- + ---------------------| + - - --------------------- - -------------------
3 6 ________________ | ________________ 6 | 3 6 ________________ | 6 ________________| 3 ________________ 3
3 / _____ | 3 / _____ | 3 / _____ | 3 / _____ | 3 / _____
3*\/ 62 + 6*\/ 105 \ 3*\/ 62 + 6*\/ 105 / 3*\/ 62 + 6*\/ 105 \ 3*\/ 62 + 6*\/ 105 / 3*\/ 62 + 6*\/ 105
$$\left(- \frac{\sqrt[3]{6 \sqrt{105} + 62}}{3} - \frac{4}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{1}{3}\right) + \left(\left(\frac{2}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{1}{3} + \frac{\sqrt[3]{6 \sqrt{105} + 62}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{6 \sqrt{105} + 62}}{6} + \frac{2 \sqrt{3}}{3 \sqrt[3]{6 \sqrt{105} + 62}}\right)\right) + \left(\frac{2}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{1}{3} + \frac{\sqrt[3]{6 \sqrt{105} + 62}}{6} + i \left(- \frac{2 \sqrt{3}}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{\sqrt{3} \sqrt[3]{6 \sqrt{105} + 62}}{6}\right)\right)\right)$$
=
/ ________________\ / ________________ \
| ___ ___ 3 / _____ | | ___ 3 / _____ ___ |
| 2*\/ 3 \/ 3 *\/ 62 + 6*\/ 105 | | \/ 3 *\/ 62 + 6*\/ 105 2*\/ 3 |
1 + I*|- --------------------- + -------------------------| + I*|- ------------------------- + ---------------------|
| ________________ 6 | | 6 ________________|
| 3 / _____ | | 3 / _____ |
\ 3*\/ 62 + 6*\/ 105 / \ 3*\/ 62 + 6*\/ 105 /
$$1 + i \left(- \frac{\sqrt{3} \sqrt[3]{6 \sqrt{105} + 62}}{6} + \frac{2 \sqrt{3}}{3 \sqrt[3]{6 \sqrt{105} + 62}}\right) + i \left(- \frac{2 \sqrt{3}}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{\sqrt{3} \sqrt[3]{6 \sqrt{105} + 62}}{6}\right)$$
producto
/ ________________ / ________________\\ / ________________ / ________________ \\ / ________________\ | 3 / _____ | ___ ___ 3 / _____ || | 3 / _____ | ___ 3 / _____ ___ || | 3 / _____ | |1 \/ 62 + 6*\/ 105 2 | 2*\/ 3 \/ 3 *\/ 62 + 6*\/ 105 || |1 \/ 62 + 6*\/ 105 2 | \/ 3 *\/ 62 + 6*\/ 105 2*\/ 3 || |1 4 \/ 62 + 6*\/ 105 | |- + ------------------- + --------------------- + I*|- --------------------- + -------------------------||*|- + ------------------- + --------------------- + I*|- ------------------------- + ---------------------||*|- - --------------------- - -------------------| |3 6 ________________ | ________________ 6 || |3 6 ________________ | 6 ________________|| |3 ________________ 3 | | 3 / _____ | 3 / _____ || | 3 / _____ | 3 / _____ || | 3 / _____ | \ 3*\/ 62 + 6*\/ 105 \ 3*\/ 62 + 6*\/ 105 // \ 3*\/ 62 + 6*\/ 105 \ 3*\/ 62 + 6*\/ 105 // \ 3*\/ 62 + 6*\/ 105 /
$$\left(\frac{2}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{1}{3} + \frac{\sqrt[3]{6 \sqrt{105} + 62}}{6} + i \left(- \frac{2 \sqrt{3}}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{\sqrt{3} \sqrt[3]{6 \sqrt{105} + 62}}{6}\right)\right) \left(\frac{2}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{1}{3} + \frac{\sqrt[3]{6 \sqrt{105} + 62}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{6 \sqrt{105} + 62}}{6} + \frac{2 \sqrt{3}}{3 \sqrt[3]{6 \sqrt{105} + 62}}\right)\right) \left(- \frac{\sqrt[3]{6 \sqrt{105} + 62}}{3} - \frac{4}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{1}{3}\right)$$
=
-5
$$-5$$
-5
Respuesta rápida
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________________ / ________________\
3 / _____ | ___ ___ 3 / _____ |
1 \/ 62 + 6*\/ 105 2 | 2*\/ 3 \/ 3 *\/ 62 + 6*\/ 105 |
x1 = - + ------------------- + --------------------- + I*|- --------------------- + -------------------------|
3 6 ________________ | ________________ 6 |
3 / _____ | 3 / _____ |
3*\/ 62 + 6*\/ 105 \ 3*\/ 62 + 6*\/ 105 /
$$x_{1} = \frac{2}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{1}{3} + \frac{\sqrt[3]{6 \sqrt{105} + 62}}{6} + i \left(- \frac{2 \sqrt{3}}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{\sqrt{3} \sqrt[3]{6 \sqrt{105} + 62}}{6}\right)$$
________________ / ________________ \
3 / _____ | ___ 3 / _____ ___ |
1 \/ 62 + 6*\/ 105 2 | \/ 3 *\/ 62 + 6*\/ 105 2*\/ 3 |
x2 = - + ------------------- + --------------------- + I*|- ------------------------- + ---------------------|
3 6 ________________ | 6 ________________|
3 / _____ | 3 / _____ |
3*\/ 62 + 6*\/ 105 \ 3*\/ 62 + 6*\/ 105 /
$$x_{2} = \frac{2}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{1}{3} + \frac{\sqrt[3]{6 \sqrt{105} + 62}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{6 \sqrt{105} + 62}}{6} + \frac{2 \sqrt{3}}{3 \sqrt[3]{6 \sqrt{105} + 62}}\right)$$
________________
3 / _____
1 4 \/ 62 + 6*\/ 105
x3 = - - --------------------- - -------------------
3 ________________ 3
3 / _____
3*\/ 62 + 6*\/ 105
$$x_{3} = - \frac{\sqrt[3]{6 \sqrt{105} + 62}}{3} - \frac{4}{3 \sqrt[3]{6 \sqrt{105} + 62}} + \frac{1}{3}$$
x3 = -(6*sqrt(105) + 62)^(1/3)/3 - 4/(3*(6*sqrt(105) + 62)^(1/3)) + 1/3
Respuesta numérica
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x1 = 1.29715650817742 + 1.20562515060291*i
x2 = -1.59431301635485
x3 = 1.29715650817742 - 1.20562515060291*i
x3 = 1.29715650817742 - 1.20562515060291*i