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Ecuación 3*x^2+13*x-10=0
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Ecuación 8-x^2=0
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Expresiones idénticas
- (catorce / cinco)*x^ tres + dos *x^ dos + diecinueve *x-(treinta y siete / diez)= cero
- (14 dividir por 5) multiplicar por x al cubo más 2 multiplicar por x al cuadrado más 19 multiplicar por x menos (37 dividir por 10) es igual a 0
- ( cotangente de angente de orce dividir por cinco) multiplicar por x en el grado tres más dos multiplicar por x en el grado dos más diecinueve multiplicar por x menos (treinta y siete dividir por diez) es igual a cero
- (14/5)*x3+2*x2+19*x-(37/10)=0
- 14/5*x3+2*x2+19*x-37/10=0
- (14/5)*x³+2*x²+19*x-(37/10)=0
- (14/5)*x en el grado 3+2*x en el grado 2+19*x-(37/10)=0
- (14/5)x^3+2x^2+19x-(37/10)=0
- (14/5)x3+2x2+19x-(37/10)=0
- 14/5x3+2x2+19x-37/10=0
- 14/5x^3+2x^2+19x-37/10=0
- (14/5)*x^3+2*x^2+19*x-(37/10)=O
- (14 dividir por 5)*x^3+2*x^2+19*x-(37 dividir por 10)=0
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Expresiones semejantes
- (14/5)*x^3+2*x^2-19*x-(37/10)=0
- (14/5)*x^3+2*x^2+19*x+(37/10)=0
- (14/5)*x^3-2*x^2+19*x-(37/10)=0
(14/5)*x^3+2*x^2+19*x-(37/10)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 14*x 2 37 ----- + 2*x + 19*x - -- = 0 5 10
$$\left(19 x + \left(\frac{14 x^{3}}{5} + 2 x^{2}\right)\right) - \frac{37}{10} = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(19 x + \left(\frac{14 x^{3}}{5} + 2 x^{2}\right)\right) - \frac{37}{10} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{5 x^{2}}{7} + \frac{95 x}{14} - \frac{37}{28} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{5}{7}$$
$$q = \frac{c}{a}$$
$$q = \frac{95}{14}$$
$$v = \frac{d}{a}$$
$$v = - \frac{37}{28}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{5}{7}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{95}{14}$$
$$x_{1} x_{2} x_{3} = - \frac{37}{28}$$
$$\left(19 x + \left(\frac{14 x^{3}}{5} + 2 x^{2}\right)\right) - \frac{37}{10} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{5 x^{2}}{7} + \frac{95 x}{14} - \frac{37}{28} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{5}{7}$$
$$q = \frac{c}{a}$$
$$q = \frac{95}{14}$$
$$v = \frac{d}{a}$$
$$v = - \frac{37}{28}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{5}{7}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{95}{14}$$
$$x_{1} x_{2} x_{3} = - \frac{37}{28}$$
Respuesta rápida
[src]
________________________ / ________________________\
/ ___________ | / ___________ |
/ 107801 \/ 159829761 | ___ / 107801 \/ 159829761 |
3 / ------ + ------------- | ___ \/ 3 *3 / ------ + ------------- |
5 \/ 74088 3528 1945 | 1945*\/ 3 \/ 74088 3528 |
x1 = - -- - ----------------------------- + ---------------------------------- + I*|- ---------------------------------- - -----------------------------------|
21 2 ________________________ | ________________________ 2 |
/ ___________ | / ___________ |
/ 107801 \/ 159829761 | / 107801 \/ 159829761 |
1764*3 / ------ + ------------- | 1764*3 / ------ + ------------- |
\/ 74088 3528 \ \/ 74088 3528 /
$$x_{1} = - \frac{\sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2} - \frac{5}{21} + \frac{1945}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2} - \frac{1945 \sqrt{3}}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}\right)$$
________________________ / ________________________ \
/ ___________ | / ___________ |
/ 107801 \/ 159829761 | ___ / 107801 \/ 159829761 |
3 / ------ + ------------- |\/ 3 *3 / ------ + ------------- ___ |
5 \/ 74088 3528 1945 | \/ 74088 3528 1945*\/ 3 |
x2 = - -- - ----------------------------- + ---------------------------------- + I*|----------------------------------- + ----------------------------------|
21 2 ________________________ | 2 ________________________|
/ ___________ | / ___________ |
/ 107801 \/ 159829761 | / 107801 \/ 159829761 |
1764*3 / ------ + ------------- | 1764*3 / ------ + ------------- |
\/ 74088 3528 \ \/ 74088 3528 /
$$x_{2} = - \frac{\sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2} - \frac{5}{21} + \frac{1945}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} + i \left(\frac{1945 \sqrt{3}}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} + \frac{\sqrt{3} \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2}\right)$$
________________________
/ ___________
5 / 107801 \/ 159829761 1945
x3 = - -- + 3 / ------ + ------------- - ---------------------------------
21 \/ 74088 3528 ________________________
/ ___________
/ 107801 \/ 159829761
882*3 / ------ + -------------
\/ 74088 3528
$$x_{3} = - \frac{1945}{882 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} - \frac{5}{21} + \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}$$
x3 = -1945/(882*(107801/74088 + sqrt(159829761)/3528)^(1/3)) - 5/21 + (107801/74088 + sqrt(159829761)/3528)^(1/3)
Suma y producto de raíces
[src]
suma
________________________ / ________________________\ ________________________ / ________________________ \
/ ___________ | / ___________ | / ___________ | / ___________ |
/ 107801 \/ 159829761 | ___ / 107801 \/ 159829761 | / 107801 \/ 159829761 | ___ / 107801 \/ 159829761 | ________________________
3 / ------ + ------------- | ___ \/ 3 *3 / ------ + ------------- | 3 / ------ + ------------- |\/ 3 *3 / ------ + ------------- ___ | / ___________
5 \/ 74088 3528 1945 | 1945*\/ 3 \/ 74088 3528 | 5 \/ 74088 3528 1945 | \/ 74088 3528 1945*\/ 3 | 5 / 107801 \/ 159829761 1945
- -- - ----------------------------- + ---------------------------------- + I*|- ---------------------------------- - -----------------------------------| + - -- - ----------------------------- + ---------------------------------- + I*|----------------------------------- + ----------------------------------| + - -- + 3 / ------ + ------------- - ---------------------------------
21 2 ________________________ | ________________________ 2 | 21 2 ________________________ | 2 ________________________| 21 \/ 74088 3528 ________________________
/ ___________ | / ___________ | / ___________ | / ___________ | / ___________
/ 107801 \/ 159829761 | / 107801 \/ 159829761 | / 107801 \/ 159829761 | / 107801 \/ 159829761 | / 107801 \/ 159829761
1764*3 / ------ + ------------- | 1764*3 / ------ + ------------- | 1764*3 / ------ + ------------- | 1764*3 / ------ + ------------- | 882*3 / ------ + -------------
\/ 74088 3528 \ \/ 74088 3528 / \/ 74088 3528 \ \/ 74088 3528 / \/ 74088 3528
$$\left(- \frac{1945}{882 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} - \frac{5}{21} + \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2} - \frac{5}{21} + \frac{1945}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2} - \frac{1945 \sqrt{3}}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2} - \frac{5}{21} + \frac{1945}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} + i \left(\frac{1945 \sqrt{3}}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} + \frac{\sqrt{3} \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2}\right)\right)\right)$$
=
/ ________________________ \ / ________________________\
| / ___________ | | / ___________ |
| ___ / 107801 \/ 159829761 | | ___ / 107801 \/ 159829761 |
|\/ 3 *3 / ------ + ------------- ___ | | ___ \/ 3 *3 / ------ + ------------- |
5 | \/ 74088 3528 1945*\/ 3 | | 1945*\/ 3 \/ 74088 3528 |
- - + I*|----------------------------------- + ----------------------------------| + I*|- ---------------------------------- - -----------------------------------|
7 | 2 ________________________| | ________________________ 2 |
| / ___________ | | / ___________ |
| / 107801 \/ 159829761 | | / 107801 \/ 159829761 |
| 1764*3 / ------ + ------------- | | 1764*3 / ------ + ------------- |
\ \/ 74088 3528 / \ \/ 74088 3528 /
$$- \frac{5}{7} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2} - \frac{1945 \sqrt{3}}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}\right) + i \left(\frac{1945 \sqrt{3}}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} + \frac{\sqrt{3} \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2}\right)$$
producto
/ ________________________ / ________________________\\ / ________________________ / ________________________ \\ | / ___________ | / ___________ || | / ___________ | / ___________ || | / 107801 \/ 159829761 | ___ / 107801 \/ 159829761 || | / 107801 \/ 159829761 | ___ / 107801 \/ 159829761 || / ________________________ \ | 3 / ------ + ------------- | ___ \/ 3 *3 / ------ + ------------- || | 3 / ------ + ------------- |\/ 3 *3 / ------ + ------------- ___ || | / ___________ | | 5 \/ 74088 3528 1945 | 1945*\/ 3 \/ 74088 3528 || | 5 \/ 74088 3528 1945 | \/ 74088 3528 1945*\/ 3 || | 5 / 107801 \/ 159829761 1945 | |- -- - ----------------------------- + ---------------------------------- + I*|- ---------------------------------- - -----------------------------------||*|- -- - ----------------------------- + ---------------------------------- + I*|----------------------------------- + ----------------------------------||*|- -- + 3 / ------ + ------------- - ---------------------------------| | 21 2 ________________________ | ________________________ 2 || | 21 2 ________________________ | 2 ________________________|| | 21 \/ 74088 3528 ________________________| | / ___________ | / ___________ || | / ___________ | / ___________ || | / ___________ | | / 107801 \/ 159829761 | / 107801 \/ 159829761 || | / 107801 \/ 159829761 | / 107801 \/ 159829761 || | / 107801 \/ 159829761 | | 1764*3 / ------ + ------------- | 1764*3 / ------ + ------------- || | 1764*3 / ------ + ------------- | 1764*3 / ------ + ------------- || | 882*3 / ------ + ------------- | \ \/ 74088 3528 \ \/ 74088 3528 // \ \/ 74088 3528 \ \/ 74088 3528 // \ \/ 74088 3528 /
$$\left(- \frac{\sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2} - \frac{5}{21} + \frac{1945}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} + i \left(\frac{1945 \sqrt{3}}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} + \frac{\sqrt{3} \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2} - \frac{5}{21} + \frac{1945}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}{2} - \frac{1945 \sqrt{3}}{1764 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}}\right)\right) \left(- \frac{1945}{882 \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}} - \frac{5}{21} + \sqrt[3]{\frac{107801}{74088} + \frac{\sqrt{159829761}}{3528}}\right)$$
=
37 -- 28
$$\frac{37}{28}$$
37/28
Respuesta numérica
[src]
x1 = -0.452107837434194 - 2.59866320182721*i
x2 = 0.189929960582673
x3 = -0.452107837434194 + 2.59866320182721*i
x3 = -0.452107837434194 + 2.59866320182721*i