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Ecuación x+9=0
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Ecuación 9x-4x+39=94
- Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
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- x3-4*x2+1,75*x-16=0
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- x en el grado 3-4*x en el grado 2+1,75*x-16=0
- x^3-4x^2+1,75x-16=0
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- x^3-4*x^2+1,75*x-16=O
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Expresiones semejantes
- x^3-4*x^2+1,75*x+16=0
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x^3-4*x^2+1,75*x-16=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 7*x
x - 4*x + --- - 16 = 0
4
$$\left(\frac{7 x}{4} + \left(x^{3} - 4 x^{2}\right)\right) - 16 = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = \frac{7}{4}$$
$$v = \frac{d}{a}$$
$$v = -16$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 4$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{7}{4}$$
$$x_{1} x_{2} x_{3} = -16$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = \frac{7}{4}$$
$$v = \frac{d}{a}$$
$$v = -16$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 4$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{7}{4}$$
$$x_{1} x_{2} x_{3} = -16$$
Suma y producto de raíces
[src]
suma
__________________ / __________________ \ __________________ / __________________ \
/ ________ | / ________ | / ________ | / ________ |
/ 497 \/ 430293 | ___ / 497 \/ 430293 | / 497 \/ 430293 | ___ / 497 \/ 430293 | __________________
3 / --- + ---------- | \/ 3 *3 / --- + ---------- ___ | 3 / --- + ---------- |\/ 3 *3 / --- + ---------- ___ | / ________
4 43 \/ 54 72 | \/ 54 72 43*\/ 3 | 4 43 \/ 54 72 | \/ 54 72 43*\/ 3 | 4 / 497 \/ 430293 43
- - -------------------------- - ----------------------- + I*|- ----------------------------- + --------------------------| + - - -------------------------- - ----------------------- + I*|----------------------------- - --------------------------| + - + 3 / --- + ---------- + --------------------------
3 __________________ 2 | 2 __________________| 3 __________________ 2 | 2 __________________| 3 \/ 54 72 __________________
/ ________ | / ________ | / ________ | / ________ | / ________
/ 497 \/ 430293 | / 497 \/ 430293 | / 497 \/ 430293 | / 497 \/ 430293 | / 497 \/ 430293
72*3 / --- + ---------- | 72*3 / --- + ---------- | 72*3 / --- + ---------- | 72*3 / --- + ---------- | 36*3 / --- + ----------
\/ 54 72 \ \/ 54 72 / \/ 54 72 \ \/ 54 72 / \/ 54 72
$$\left(\frac{43}{36 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{4}{3} + \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2} - \frac{43}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2} + \frac{43 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2} - \frac{43}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{4}{3} + i \left(- \frac{43 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2}\right)\right)\right)$$
=
/ __________________ \ / __________________ \
| / ________ | | / ________ |
| ___ / 497 \/ 430293 | | ___ / 497 \/ 430293 |
|\/ 3 *3 / --- + ---------- ___ | | \/ 3 *3 / --- + ---------- ___ |
| \/ 54 72 43*\/ 3 | | \/ 54 72 43*\/ 3 |
4 + I*|----------------------------- - --------------------------| + I*|- ----------------------------- + --------------------------|
| 2 __________________| | 2 __________________|
| / ________ | | / ________ |
| / 497 \/ 430293 | | / 497 \/ 430293 |
| 72*3 / --- + ---------- | | 72*3 / --- + ---------- |
\ \/ 54 72 / \ \/ 54 72 /
$$4 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2} + \frac{43 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}\right) + i \left(- \frac{43 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2}\right)$$
producto
/ __________________ / __________________ \\ / __________________ / __________________ \\ | / ________ | / ________ || | / ________ | / ________ || | / 497 \/ 430293 | ___ / 497 \/ 430293 || | / 497 \/ 430293 | ___ / 497 \/ 430293 || / __________________ \ | 3 / --- + ---------- | \/ 3 *3 / --- + ---------- ___ || | 3 / --- + ---------- |\/ 3 *3 / --- + ---------- ___ || | / ________ | |4 43 \/ 54 72 | \/ 54 72 43*\/ 3 || |4 43 \/ 54 72 | \/ 54 72 43*\/ 3 || |4 / 497 \/ 430293 43 | |- - -------------------------- - ----------------------- + I*|- ----------------------------- + --------------------------||*|- - -------------------------- - ----------------------- + I*|----------------------------- - --------------------------||*|- + 3 / --- + ---------- + --------------------------| |3 __________________ 2 | 2 __________________|| |3 __________________ 2 | 2 __________________|| |3 \/ 54 72 __________________| | / ________ | / ________ || | / ________ | / ________ || | / ________ | | / 497 \/ 430293 | / 497 \/ 430293 || | / 497 \/ 430293 | / 497 \/ 430293 || | / 497 \/ 430293 | | 72*3 / --- + ---------- | 72*3 / --- + ---------- || | 72*3 / --- + ---------- | 72*3 / --- + ---------- || | 36*3 / --- + ---------- | \ \/ 54 72 \ \/ 54 72 // \ \/ 54 72 \ \/ 54 72 // \ \/ 54 72 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2} - \frac{43}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{4}{3} + i \left(- \frac{43 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2} - \frac{43}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2} + \frac{43 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}\right)\right) \left(\frac{43}{36 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{4}{3} + \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}\right)$$
=
16
$$16$$
16
Respuesta rápida
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__________________ / __________________ \
/ ________ | / ________ |
/ 497 \/ 430293 | ___ / 497 \/ 430293 |
3 / --- + ---------- | \/ 3 *3 / --- + ---------- ___ |
4 43 \/ 54 72 | \/ 54 72 43*\/ 3 |
x1 = - - -------------------------- - ----------------------- + I*|- ----------------------------- + --------------------------|
3 __________________ 2 | 2 __________________|
/ ________ | / ________ |
/ 497 \/ 430293 | / 497 \/ 430293 |
72*3 / --- + ---------- | 72*3 / --- + ---------- |
\/ 54 72 \ \/ 54 72 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2} - \frac{43}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2} + \frac{43 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}\right)$$
__________________ / __________________ \
/ ________ | / ________ |
/ 497 \/ 430293 | ___ / 497 \/ 430293 |
3 / --- + ---------- |\/ 3 *3 / --- + ---------- ___ |
4 43 \/ 54 72 | \/ 54 72 43*\/ 3 |
x2 = - - -------------------------- - ----------------------- + I*|----------------------------- - --------------------------|
3 __________________ 2 | 2 __________________|
/ ________ | / ________ |
/ 497 \/ 430293 | / 497 \/ 430293 |
72*3 / --- + ---------- | 72*3 / --- + ---------- |
\/ 54 72 \ \/ 54 72 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2} - \frac{43}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{4}{3} + i \left(- \frac{43 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}}{2}\right)$$
__________________
/ ________
4 / 497 \/ 430293 43
x3 = - + 3 / --- + ---------- + --------------------------
3 \/ 54 72 __________________
/ ________
/ 497 \/ 430293
36*3 / --- + ----------
\/ 54 72
$$x_{3} = \frac{43}{36 \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}} + \frac{4}{3} + \sqrt[3]{\frac{\sqrt{430293}}{72} + \frac{497}{54}}$$
x3 = 43/(36*(sqrt(430293)/72 + 497/54)^(1/3)) + 4/3 + (sqrt(430293)/72 + 497/54)^(1/3)
Respuesta numérica
[src]
x1 = -0.211193223173952 - 1.89033158941373*i
x2 = -0.211193223173952 + 1.89033158941373*i
x3 = 4.4223864463479
x3 = 4.4223864463479