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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 3^x=27
- 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
- dos / tres (uno /3x- uno / dos)= seis x- dos (x- once / cuatro) dos *x^ dos +6*x+ nueve = cero
- 2 dividir por 3(1 dividir por 3x menos 1 dividir por 2) es igual a 6x menos 2(x menos 11 dividir por 4)2 multiplicar por x al cuadrado más 6 multiplicar por x más 9 es igual a 0
- dos dividir por tres (uno dividir por 3x menos uno dividir por dos) es igual a seis x menos dos (x menos once dividir por cuatro) dos multiplicar por x en el grado dos más 6 multiplicar por x más nueve es igual a cero
- 2/3(1/3x-1/2)=6x-2(x-11/4)2*x2+6*x+9=0
- 2/31/3x-1/2=6x-2x-11/42*x2+6*x+9=0
- 2/3(1/3x-1/2)=6x-2(x-11/4)2*x²+6*x+9=0
- 2/3(1/3x-1/2)=6x-2(x-11/4)2*x en el grado 2+6*x+9=0
- 2/3(1/3x-1/2)=6x-2(x-11/4)2x^2+6x+9=0
- 2/3(1/3x-1/2)=6x-2(x-11/4)2x2+6x+9=0
- 2/31/3x-1/2=6x-2x-11/42x2+6x+9=0
- 2/31/3x-1/2=6x-2x-11/42x^2+6x+9=0
- 2/3(1/3x-1/2)=6x-2(x-11/4)2*x^2+6*x+9=O
- 2 dividir por 3(1 dividir por 3x-1 dividir por 2)=6x-2(x-11 dividir por 4)2*x^2+6*x+9=0
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Expresiones semejantes
- 2/3(1/3x-1/2)=6x+2(x-11/4)2*x^2+6*x+9=0
- 2/3*(1/3*x-1/2)=0
- 2/3(1/3x-1/2)=6x-2(x+11/4)2*x^2+6*x+9=0
- 2/3(1/3x-1/2)=6x-2(x-11/4)2*x^2+6*x-9=0
- 2/3(1/3x-1/2)=6x-2(x-11/4)2*x^2-6*x+9=0
- 2/3*(1/3x-1/2)=4x+2.1/2
- 2/3(1/3x+1/2)=6x-2(x-11/4)2*x^2+6*x+9=0
2/3(1/3x-1/2)=6x-2(x-11/4)2*x^2+6*x+9=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/x 1\
2*|- - -|
\3 2/ 2
--------- = 6*x - 2*(x - 11/4)*2*x + 6*x + 9
3
$$\frac{2 \left(\frac{x}{3} - \frac{1}{2}\right)}{3} = \left(6 x + \left(- x^{2} \cdot 2 \cdot 2 \left(x - \frac{11}{4}\right) + 6 x\right)\right) + 9$$
Suma y producto de raíces
[src]
suma
____________________ / ____________________ \ ____________________ / ____________________ \
/ __________ | / __________ | / __________ | / __________ |
/ 631 \/ 71875257 | ___ / 631 \/ 71875257 | / 631 \/ 71875257 | ___ / 631 \/ 71875257 | ____________________
3 / --- + ------------ | \/ 3 *3 / --- + ------------ ___ | 3 / --- + ------------ |\/ 3 *3 / --- + ------------ ___ | / __________
11 787 \/ 192 3888 | \/ 192 3888 787*\/ 3 | 11 787 \/ 192 3888 | \/ 192 3888 787*\/ 3 | 11 / 631 \/ 71875257 787
-- - ----------------------------- - ------------------------- + I*|- ------------------------------- + -----------------------------| + -- - ----------------------------- - ------------------------- + I*|------------------------------- - -----------------------------| + -- + 3 / --- + ------------ + -----------------------------
12 ____________________ 2 | 2 ____________________| 12 ____________________ 2 | 2 ____________________| 12 \/ 192 3888 ____________________
/ __________ | / __________ | / __________ | / __________ | / __________
/ 631 \/ 71875257 | / 631 \/ 71875257 | / 631 \/ 71875257 | / 631 \/ 71875257 | / 631 \/ 71875257
864*3 / --- + ------------ | 864*3 / --- + ------------ | 864*3 / --- + ------------ | 864*3 / --- + ------------ | 432*3 / --- + ------------
\/ 192 3888 \ \/ 192 3888 / \/ 192 3888 \ \/ 192 3888 / \/ 192 3888
$$\left(\frac{11}{12} + \frac{787}{432 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2} - \frac{787}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \frac{11}{12} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2} + \frac{787 \sqrt{3}}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2} - \frac{787}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \frac{11}{12} + i \left(- \frac{787 \sqrt{3}}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2}\right)\right)\right)$$
=
/ ____________________ \ / ____________________ \
| / __________ | | / __________ |
| ___ / 631 \/ 71875257 | | ___ / 631 \/ 71875257 |
|\/ 3 *3 / --- + ------------ ___ | | \/ 3 *3 / --- + ------------ ___ |
11 | \/ 192 3888 787*\/ 3 | | \/ 192 3888 787*\/ 3 |
-- + I*|------------------------------- - -----------------------------| + I*|- ------------------------------- + -----------------------------|
4 | 2 ____________________| | 2 ____________________|
| / __________ | | / __________ |
| / 631 \/ 71875257 | | / 631 \/ 71875257 |
| 864*3 / --- + ------------ | | 864*3 / --- + ------------ |
\ \/ 192 3888 / \ \/ 192 3888 /
$$\frac{11}{4} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2} + \frac{787 \sqrt{3}}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}\right) + i \left(- \frac{787 \sqrt{3}}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2}\right)$$
producto
/ ____________________ / ____________________ \\ / ____________________ / ____________________ \\ | / __________ | / __________ || | / __________ | / __________ || | / 631 \/ 71875257 | ___ / 631 \/ 71875257 || | / 631 \/ 71875257 | ___ / 631 \/ 71875257 || / ____________________ \ | 3 / --- + ------------ | \/ 3 *3 / --- + ------------ ___ || | 3 / --- + ------------ |\/ 3 *3 / --- + ------------ ___ || | / __________ | |11 787 \/ 192 3888 | \/ 192 3888 787*\/ 3 || |11 787 \/ 192 3888 | \/ 192 3888 787*\/ 3 || |11 / 631 \/ 71875257 787 | |-- - ----------------------------- - ------------------------- + I*|- ------------------------------- + -----------------------------||*|-- - ----------------------------- - ------------------------- + I*|------------------------------- - -----------------------------||*|-- + 3 / --- + ------------ + -----------------------------| |12 ____________________ 2 | 2 ____________________|| |12 ____________________ 2 | 2 ____________________|| |12 \/ 192 3888 ____________________| | / __________ | / __________ || | / __________ | / __________ || | / __________ | | / 631 \/ 71875257 | / 631 \/ 71875257 || | / 631 \/ 71875257 | / 631 \/ 71875257 || | / 631 \/ 71875257 | | 864*3 / --- + ------------ | 864*3 / --- + ------------ || | 864*3 / --- + ------------ | 864*3 / --- + ------------ || | 432*3 / --- + ------------ | \ \/ 192 3888 \ \/ 192 3888 // \ \/ 192 3888 \ \/ 192 3888 // \ \/ 192 3888 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2} - \frac{787}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \frac{11}{12} + i \left(- \frac{787 \sqrt{3}}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2} - \frac{787}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \frac{11}{12} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2} + \frac{787 \sqrt{3}}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}\right)\right) \left(\frac{11}{12} + \frac{787}{432 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}\right)$$
=
7/3
$$\frac{7}{3}$$
7/3
Respuesta rápida
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____________________ / ____________________ \
/ __________ | / __________ |
/ 631 \/ 71875257 | ___ / 631 \/ 71875257 |
3 / --- + ------------ | \/ 3 *3 / --- + ------------ ___ |
11 787 \/ 192 3888 | \/ 192 3888 787*\/ 3 |
x1 = -- - ----------------------------- - ------------------------- + I*|- ------------------------------- + -----------------------------|
12 ____________________ 2 | 2 ____________________|
/ __________ | / __________ |
/ 631 \/ 71875257 | / 631 \/ 71875257 |
864*3 / --- + ------------ | 864*3 / --- + ------------ |
\/ 192 3888 \ \/ 192 3888 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2} - \frac{787}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \frac{11}{12} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2} + \frac{787 \sqrt{3}}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}\right)$$
____________________ / ____________________ \
/ __________ | / __________ |
/ 631 \/ 71875257 | ___ / 631 \/ 71875257 |
3 / --- + ------------ |\/ 3 *3 / --- + ------------ ___ |
11 787 \/ 192 3888 | \/ 192 3888 787*\/ 3 |
x2 = -- - ----------------------------- - ------------------------- + I*|------------------------------- - -----------------------------|
12 ____________________ 2 | 2 ____________________|
/ __________ | / __________ |
/ 631 \/ 71875257 | / 631 \/ 71875257 |
864*3 / --- + ------------ | 864*3 / --- + ------------ |
\/ 192 3888 \ \/ 192 3888 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2} - \frac{787}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \frac{11}{12} + i \left(- \frac{787 \sqrt{3}}{864 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}}{2}\right)$$
____________________
/ __________
11 / 631 \/ 71875257 787
x3 = -- + 3 / --- + ------------ + -----------------------------
12 \/ 192 3888 ____________________
/ __________
/ 631 \/ 71875257
432*3 / --- + ------------
\/ 192 3888
$$x_{3} = \frac{11}{12} + \frac{787}{432 \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}} + \sqrt[3]{\frac{\sqrt{71875257}}{3888} + \frac{631}{192}}$$
x3 = 11/12 + 787/(432*(sqrt(71875257)/3888 + 631/192)^(1/3)) + (sqrt(71875257)/3888 + 631/192)^(1/3)
Respuesta numérica
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x1 = 3.71243197879058
x2 = -0.481215989395292 - 0.630039667464461*i
x3 = -0.481215989395292 + 0.630039667464461*i
x3 = -0.481215989395292 + 0.630039667464461*i