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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:
- 7*x-1*y=0
- -11*x-3*y=14
- 2*x-15*y=-1
- -18*x-6*y=-1
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Expresiones idénticas
- diez /x^ dos - dos *x+ cuatro = cero
- 10 dividir por x al cuadrado menos 2 multiplicar por x más 4 es igual a 0
- diez dividir por x en el grado dos menos dos multiplicar por x más cuatro es igual a cero
- 10/x2-2*x+4=0
- 10/x²-2*x+4=0
- 10/x en el grado 2-2*x+4=0
- 10/x^2-2x+4=0
- 10/x2-2x+4=0
- 10/x^2-2*x+4=O
- 10 dividir por x^2-2*x+4=0
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Expresiones semejantes
- 10/x^2+2*x+4=0
- 10/x^2-2*x-4=0
10/x^2-2*x+4=0 la ecuación
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Solución
Suma y producto de raíces
[src]
suma
________________ / ________________ \ ________________ / ________________ \
/ ______ | / ______ | / ______ | / ______ |
/ 151 \/ 2505 | ___ / 151 \/ 2505 | / 151 \/ 2505 | ___ / 151 \/ 2505 | ________________
3 / --- + -------- | \/ 3 *3 / --- + -------- ___ | 3 / --- + -------- |\/ 3 *3 / --- + -------- ___ | / ______
2 2 \/ 54 18 | \/ 54 18 2*\/ 3 | 2 2 \/ 54 18 | \/ 54 18 2*\/ 3 | 2 / 151 \/ 2505 4
- - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------| + - - ----------------------- - --------------------- + I*|--------------------------- - -----------------------| + - + 3 / --- + -------- + -----------------------
3 ________________ 2 | 2 ________________| 3 ________________ 2 | 2 ________________| 3 \/ 54 18 ________________
/ ______ | / ______ | / ______ | / ______ | / ______
/ 151 \/ 2505 | / 151 \/ 2505 | / 151 \/ 2505 | / 151 \/ 2505 | / 151 \/ 2505
9*3 / --- + -------- | 9*3 / --- + -------- | 9*3 / --- + -------- | 9*3 / --- + -------- | 9*3 / --- + --------
\/ 54 18 \ \/ 54 18 / \/ 54 18 \ \/ 54 18 / \/ 54 18
$$\left(\frac{4}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{2}{3} + \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{2}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{2}{3} + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2}\right)\right)\right)$$
=
/ ________________ \ / ________________ \
| / ______ | | / ______ |
| ___ / 151 \/ 2505 | | ___ / 151 \/ 2505 |
|\/ 3 *3 / --- + -------- ___ | | \/ 3 *3 / --- + -------- ___ |
| \/ 54 18 2*\/ 3 | | \/ 54 18 2*\/ 3 |
2 + I*|--------------------------- - -----------------------| + I*|- --------------------------- + -----------------------|
| 2 ________________| | 2 ________________|
| / ______ | | / ______ |
| / 151 \/ 2505 | | / 151 \/ 2505 |
| 9*3 / --- + -------- | | 9*3 / --- + -------- |
\ \/ 54 18 / \ \/ 54 18 /
$$2 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}\right) + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2}\right)$$
producto
/ ________________ / ________________ \\ / ________________ / ________________ \\ | / ______ | / ______ || | / ______ | / ______ || | / 151 \/ 2505 | ___ / 151 \/ 2505 || | / 151 \/ 2505 | ___ / 151 \/ 2505 || / ________________ \ | 3 / --- + -------- | \/ 3 *3 / --- + -------- ___ || | 3 / --- + -------- |\/ 3 *3 / --- + -------- ___ || | / ______ | |2 2 \/ 54 18 | \/ 54 18 2*\/ 3 || |2 2 \/ 54 18 | \/ 54 18 2*\/ 3 || |2 / 151 \/ 2505 4 | |- - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------||*|- - ----------------------- - --------------------- + I*|--------------------------- - -----------------------||*|- + 3 / --- + -------- + -----------------------| |3 ________________ 2 | 2 ________________|| |3 ________________ 2 | 2 ________________|| |3 \/ 54 18 ________________| | / ______ | / ______ || | / ______ | / ______ || | / ______ | | / 151 \/ 2505 | / 151 \/ 2505 || | / 151 \/ 2505 | / 151 \/ 2505 || | / 151 \/ 2505 | | 9*3 / --- + -------- | 9*3 / --- + -------- || | 9*3 / --- + -------- | 9*3 / --- + -------- || | 9*3 / --- + -------- | \ \/ 54 18 \ \/ 54 18 // \ \/ 54 18 \ \/ 54 18 // \ \/ 54 18 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{2}{3} + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{2}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}\right)\right) \left(\frac{4}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{2}{3} + \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}\right)$$
=
5
$$5$$
5
Respuesta rápida
[src]
________________ / ________________ \
/ ______ | / ______ |
/ 151 \/ 2505 | ___ / 151 \/ 2505 |
3 / --- + -------- | \/ 3 *3 / --- + -------- ___ |
2 2 \/ 54 18 | \/ 54 18 2*\/ 3 |
x1 = - - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------|
3 ________________ 2 | 2 ________________|
/ ______ | / ______ |
/ 151 \/ 2505 | / 151 \/ 2505 |
9*3 / --- + -------- | 9*3 / --- + -------- |
\/ 54 18 \ \/ 54 18 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{2}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}\right)$$
________________ / ________________ \
/ ______ | / ______ |
/ 151 \/ 2505 | ___ / 151 \/ 2505 |
3 / --- + -------- |\/ 3 *3 / --- + -------- ___ |
2 2 \/ 54 18 | \/ 54 18 2*\/ 3 |
x2 = - - ----------------------- - --------------------- + I*|--------------------------- - -----------------------|
3 ________________ 2 | 2 ________________|
/ ______ | / ______ |
/ 151 \/ 2505 | / 151 \/ 2505 |
9*3 / --- + -------- | 9*3 / --- + -------- |
\/ 54 18 \ \/ 54 18 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{2}{3} + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}}{2}\right)$$
________________
/ ______
2 / 151 \/ 2505 4
x3 = - + 3 / --- + -------- + -----------------------
3 \/ 54 18 ________________
/ ______
/ 151 \/ 2505
9*3 / --- + --------
\/ 54 18
$$x_{3} = \frac{4}{9 \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}} + \frac{2}{3} + \sqrt[3]{\frac{\sqrt{2505}}{18} + \frac{151}{54}}$$
x3 = 4/(9*(sqrt(2505)/18 + 151/54)^(1/3)) + 2/3 + (sqrt(2505)/18 + 151/54)^(1/3)
Respuesta numérica
[src]
x1 = -0.345323724014307 - 1.31872677957132*i
x2 = -0.345323724014307 + 1.31872677957132*i
x3 = 2.69064744802861
x3 = 2.69064744802861